Polyhedra in OpenSCAD

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Name Groups #Vertices Vertex orders #Faces Face orders #Edges Conway
10-Truncated Triakis Icosahedron (canonical)  dmccooeyTruncated Catalan 140 140 of 3 72 12 of 10,60 of 5 210 t10kI
132-pentagon Polyhedron  dmccooeyDerived 200 140 of 3,60 of 4 132 132 of 5 330
4-5-Truncated Deltoidal Hexecontahedron  dmccooeyTruncated Catalan 200 200 of 3 102 60 of 7,12 of 5,30 of 4 300
4-Truncated Deltoidal Icositetrahedron (canonical)  dmccooeyTruncated Catalan 80 80 of 3 42 24 of 7,18 of 4 120 t4oO
6-Truncated Joined Truncated Tetrahedron (canonical)  dmccooeyDerived 40 40 of 3 22 10 of 6,12 of 5 60 t6jtT
6-Truncated Pentakis Dodecahedron (canonical)  dmccooeyTruncated Catalan 132 120 of 3,12 of 5 80 20 of 6,60 of 5 210 t6kD
6-Truncated Tetrakis Hexahedron (canonical)  dmccooeyTruncated Catalan 54 6 of 4,48 of 3 32 8 of 6,24 of 5 84 t6kC
6-Truncated Triakis Tetrahedron (canonical)  dmccooeyTruncated Catalan 28 28 of 3 16 4 of 6,12 of 5 42 t6kT
8-Truncated Triakis Octahedron (canonical)  dmccooeyTruncated Catalan 56 56 of 3 30 6 of 8,24 of 5 84 t8kO
Another of George's polyhedra  Hart 420 420 of 5 632 60 of 6,12 of 5,560 of 3 1050 sdk5sI
Anti-Heptagonal Iris Toroid  dmccooeyRegular Triangular Toroidalconcave 14 14 of 6 28 28 of 3 40
Anti-Hexagonal Iris Toroid  dmccooeyRegular Triangular Toroidalconcave 12 12 of 6 24 24 of 3 34
Anti-Octagonal Iris Toroid #1  dmccooeyRegular Triangular Toroidalconcave 16 16 of 6 32 32 of 3 46
Anti-Octagonal Iris Toroid #2  dmccooeyRegular Triangular Toroidalconcave 16 16 of 6 32 32 of 3 46
Associahedron (canonical)  dmccooeyOther 14 14 of 3 9 6 of 5,3 of 4 21
Bilateral Pentagonal Icositetrahedron  Other 38 32 of 3,6 of 4 24 24 of 5 60
Bilinski's Dodecahedron  Otherdmccooey 14 6 of 4,8 of 3 12 12 of 4 24
Biscribed Disdyakis Dodecahedron  dmccooeyBiscribed Non-Chiral 26 6 of 8,12 of 4,8 of 6 48 48 of 3 72
Biscribed Disdyakis Triacontahedron  dmccooeyBiscribed Non-Chiral 62 30 of 4,20 of 6,12 of 10 120 120 of 3 180
Biscribed Dual Snub Truncated Icosahedron  dmccooeyBiscribed Chiral 272 240 of 3,20 of 6,12 of 5 180 180 of 5 450
Biscribed Dual Snub Truncated Octahedron  dmccooeyBiscribed Chiral 110 6 of 4,96 of 3,8 of 6 72 72 of 5 180
Biscribed Hexpropello Cube (dextro)  dmccooeyBiscribed Chiral 56 56 of 3 30 24 of 6,6 of 4 84
Biscribed Hexpropello Dodecahedron (dextro)  dmccooeyBiscribed Chiral 140 140 of 3 72 60 of 6,12 of 5 210
Biscribed L-Propello L-Snub Cube  dmccooeyBiscribed Chiral 144 120 of 4,24 of 5 158 126 of 4,32 of 3 300
Biscribed L-Propello R-pentagonal Icositetrahedron  dmccooeyBiscribed Chiral 158 126 of 4,32 of 3 144 24 of 5,120 of 4 300
Biscribed Orthokis Propello Cube  dmccooeyBiscribed Chiral 38 6 of 4,24 of 5,8 of 3 48 24 of 4,24 of 3 84
Biscribed Orthokis Propello Dodecahedron  dmccooeyBiscribed Chiral 92 72 of 5,20 of 3 120 60 of 4,60 of 3 210
Biscribed Orthotruncated Propello Icosahedron  dmccooeyBiscribed Chiral 120 60 of 4,60 of 3 92 72 of 5,20 of 3 210
Biscribed Orthotruncated Propello Octahedron  dmccooeyBiscribed Chiral 48 24 of 3,24 of 4 38 24 of 5,6 of 4,8 of 3 84
Biscribed pentagonal Hexecontahedron (dextro)  dmccooeyBiscribed Chiral 92 80 of 3,12 of 5 60 60 of 5 150
Biscribed pentagonal Icositetrahedron (dextro)  dmccooeyBiscribed Chiral 38 6 of 4,32 of 3 24 24 of 5 60
Biscribed Pentakis Dodecahedron  dmccooeyBiscribed Non-Chiral 32 20 of 6,12 of 5 60 60 of 3 90
Biscribed Pentakis Snub Dodecahedron (laevo)  dmccooeyBiscribed Chiral 72 60 of 6,12 of 5 140 140 of 3 210
Biscribed Propello Cube  dmccooeyBiscribed Chiral 32 24 of 4,8 of 3 30 30 of 4 60
Biscribed Propello Disdyakis Dodecahedron  dmccooeyBiscribed Chiral 170 6 of 8,156 of 4,8 of 6 192 144 of 4,48 of 3 360
Biscribed Propello Disdyakis Triacontahedron  dmccooeyBiscribed Chiral 422 390 of 4,20 of 6,12 of 10 480 360 of 4,120 of 3 900
Biscribed Propello Dodecahedron  dmccooeyBiscribed Chiral 80 60 of 4,20 of 3 72 12 of 5,60 of 4 150
Biscribed Propello Icosahedron  dmccooeyBiscribed Chiral 72 60 of 4,12 of 5 80 60 of 4,20 of 3 150
Biscribed Propello Octahedron  dmccooeyBiscribed Chiral 30 30 of 4 32 24 of 4,8 of 3 60
Biscribed Propello Pentakis Dodecahedron  dmccooeyBiscribed Chiral 212 180 of 4,20 of 6,12 of 5 240 180 of 4,60 of 3 450
Biscribed Propello Tetrahedron  dmccooeyBiscribed Chiral 16 12 of 4,4 of 3 16 12 of 4,4 of 3 30
Biscribed Propello Tetrakis Hexahedron  dmccooeyBiscribed Chiral 86 78 of 4,8 of 6 96 72 of 4,24 of 3 180
Biscribed Propello Truncated Cuboctahedron  dmccooeyBiscribed Chiral 192 144 of 4,48 of 3 170 6 of 8,8 of 6,156 of 4 360
Biscribed Propello Truncated Icosahedron  dmccooeyBiscribed Chiral 240 180 of 4,60 of 3 212 20 of 6,12 of 5,180 of 4 450
Biscribed Propello Truncated Icosidodecahedron  dmccooeyBiscribed Chiral 480 360 of 4,120 of 3 422 12 of 10,20 of 6,390 of 4 900
Biscribed Propello Truncated Octahedron  dmccooeyBiscribed Chiral 96 72 of 4,24 of 3 86 8 of 6,78 of 4 180
Biscribed Snub Cube (laevo)  dmccooeyBiscribed Chiral 24 24 of 5 38 6 of 4,32 of 3 60
Biscribed Snub Dodecahedron (laevo)  dmccooeyBiscribed Chiral 60 60 of 5 92 12 of 5,80 of 3 150
Biscribed Snub Truncated Icosahedron  dmccooeyBiscribed Chiral 180 180 of 5 272 20 of 6,12 of 5,240 of 3 450
Biscribed Snub Truncated Octahedron  dmccooeyBiscribed Chiral 72 72 of 5 110 8 of 6,6 of 4,96 of 3 180
Biscribed Tetrakis Hexahedron  dmccooeyBiscribed Non-Chiral 14 6 of 4,8 of 6 24 24 of 3 36
Biscribed Tetrakis Snub Cube (laevo)  dmccooeyBiscribed Chiral 30 6 of 4,24 of 6 56 56 of 3 84
Biscribed Truncated Cuboctahedron  dmccooeyBiscribed Non-Chiral 48 48 of 3 26 6 of 8,8 of 6,12 of 4 72
Biscribed Truncated Icosahedron  dmccooeyBiscribed Non-Chiral 60 60 of 3 32 20 of 6,12 of 5 90
Biscribed Truncated Icosidodecahedron  dmccooeyBiscribed Non-Chiral 120 120 of 3 62 12 of 10,20 of 6,30 of 4 180
Biscribed Truncated Octahedron  dmccooeyBiscribed Non-Chiral 24 24 of 3 14 8 of 6,6 of 4 36
Bisymmetric Hendecahedron  Space-filling 11 4 of 3,7 of 4 11 7 of 4,4 of 3 20
Borromean Rings  dmccooeyRegular Tetragonal Toroidalconcave 36 36 of 4 36 36 of 4 70
Cairo-Tiling Toroid with 16 faces (type A) (8 faces overarching)  dmccooeyNon-Regular Toroidalconcave 24 16 of 3,8 of 4 16 16 of 5 38
Cairo-Tiling Toroid with 16 faces (type B) (square form)  dmccooeyNon-Regular Toroidalconcave 24 16 of 3,8 of 4 16 16 of 5 38
Cairo-Tiling Toroid with 16 faces (type C) (boomerang form)  dmccooeyNon-Regular Toroidalconcave 24 8 of 4,16 of 3 16 16 of 5 38
Cairo-Tiling Toroid with 8 overarching faces (version 1)  dmccooeyNon-Regular Toroidalconcave 12 8 of 3,4 of 4 8 8 of 5 18
Canonical Joined Truncated Icosahedron  dmccooeyOther 92 20 of 6,60 of 3,12 of 5 90 90 of 4 180 jtI
Chamfered Cube (all edges equal)  dmccooeyChamfered 32 32 of 3 18 12 of 6,6 of 4 48 cC
Chamfered Dodecahedron (all edges equal)  dmccooeyChamfered 80 80 of 3 42 30 of 6,12 of 5 120 cD
Chamfered Icosahedron (all edges equal)  dmccooeyChamfered 72 12 of 5,60 of 3 50 30 of 6,20 of 3 120 cI
Chamfered Octahedron (all edges equal)  dmccooeyChamfered 30 6 of 4,24 of 3 20 12 of 6,8 of 3 48 cO
Chamfered Tetrahedron (all edges equal)  dmccooeyChamfered 16 16 of 3 10 6 of 6,4 of 3 24 cT
Chamfered Truncated Icosahedron (canonical)  Goldberg(2,2) dmccooeyChamferedGoldberg 240 240 of 3 122 110 of 6,12 of 5 360 ctI
Chestahedron  Other 7 4 of 3,3 of 4 7 3 of 4,4 of 3 12
Concave Dodecahedron  dmccooeyconcaveOther 20 20 of 3 12 12 of 5 30
Császár Polyhedron (version 4)  dmccooeyRegular Triangular Toroidalconcave 7 7 of 6 14 14 of 3 19
Cube  Hexahedron dmccooeyPlatonicisohedronSpace-filling 8 8 of 3 6 6 of 4 12 C, jY3
Cube-Octahedron Compound  dmccooeyconcaveOther 14 8 of 3,6 of 4 14 6 of 4,8 of 3 26 y0.57C
Cube-Octahedron Toroid  dmccooeyNon-Regular Toroidalconcave 12 6 of 3,6 of 5 12 6 of 5,6 of 3 22
Cubitruncated Cuboctahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 48 48 of 3 20 12 of 8,8 of 6 66
Cuboctahedron  dmccooeyArchimedean 12 12 of 4 14 6 of 4,8 of 3 24 aC
Cubohemioctahedron  dmccooeyVersi-Regularconcave 12 12 of 4 10 4 of 6,6 of 4 20 k(h=-0.65,fn=[3])aC
Deltoidal Hexecontahedron  dmccooeyCatalanisohedron 62 30 of 4,20 of 3,12 of 5 60 60 of 4 120 oD
Deltoidal Icositetrahedron  dmccooeyCatalanisohedron 26 18 of 4,8 of 3 24 24 of 4 48 oO
dgtD  CW designs dgtD
Disdyakis Dodecahedron  Hexakis Octahedron dmccooeyCatalanisohedron 26 6 of 8,12 of 4,8 of 6 48 48 of 3 72 mC, mO
Disdyakis Triacontahedron  Hexakis Icosahedron dmccooeyCatalanisohedron 62 30 of 4,20 of 6,12 of 10 120 120 of 3 180 mD
Ditrigonal Dodecadodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 20 20 of 6 24 24 of 5 42
Dodecadodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 30 30 of 4 24 24 of 5 52
Dodecahedron  Goldberg(0,1) dmccooeyGoldbergPlatonicisohedron 20 20 of 3 12 12 of 5 30 D, gY3
Dodecahedron-Icosahedron Compound  dmccooeyconcaveOther 32 20 of 3,12 of 5 32 12 of 5,20 of 3 62 y0.3D
Dual Geodesic Icosahedron Pattern [16,0]  Goldberg(16,0) Dual Geodesic IcosahedraGoldberg 5120 2662 12 of 5,2550 of 6 7780 ccccD
Dual Geodesic Icosahedron Pattern [6,6]  Goldberg(6,6) Dual Geodesic IcosahedraGoldberg 2160 1082 12 of 5,1070 of 6 3240 ctktI
Dual Geodesic Icosahedron Pattern [9,0]  Goldberg(9,0) Dual Geodesic IcosahedraGoldberg 1620 812 12 of 5,800 of 6 2430 tdtdtkD
Dual Geodesic Icosahedron Pattern 1 [1,1]  Truncated Icosahedron, Goldberg(1,1) dmccooeyDual Geodesic IcosahedraGoldberg 60 60 of 3 32 20 of 6,12 of 5 90 tI, dkD
Dual Geodesic Icosahedron Pattern 10 [5,0]  Goldberg(5,0) dmccooeyDual Geodesic IcosahedraGoldberg 500 500 of 3 252 12 of 5,240 of 6 750
Dual Geodesic Icosahedron Pattern 11 [3,3]  Goldberg(3,3) dmccooeyDual Geodesic IcosahedraGoldberg 540 540 of 3 272 12 of 5,260 of 6 810 tktI
Dual Geodesic Icosahedron Pattern 12 [4,2]  Goldberg(4,2) dmccooeyDual Geodesic IcosahedraGoldberg 560 560 of 3 282 12 of 5,270 of 6 840 wcD
Dual Geodesic Icosahedron Pattern 13 [5,1]  Goldberg(5,1) dmccooeyDual Geodesic IcosahedraGoldberg 620 620 of 3 312 12 of 5,300 of 6 930
Dual Geodesic Icosahedron Pattern 14 [6,0]  Goldberg(6,0) dmccooeyDual Geodesic IcosahedraGoldberg 720 720 of 3 362 12 of 5,350 of 6 1080 ctkD, cdktI, tkt5daD
Dual Geodesic Icosahedron Pattern 15 [4,3]  Goldberg(4,3) dmccooeyDual Geodesic IcosahedraGoldberg 740 740 of 3 372 12 of 5,360 of 6 1110
Dual Geodesic Icosahedron Pattern 16 [5,2]  Goldberg(5,2) dmccooeyDual Geodesic IcosahedraGoldberg 780 780 of 3 392 12 of 5,380 of 6 1170
Dual Geodesic Icosahedron Pattern 17 [6,1]  Goldberg(6,1) dmccooeyDual Geodesic IcosahedraGoldberg 860 860 of 3 432 12 of 5,420 of 6 1290
Dual Geodesic Icosahedron Pattern 18 [4,4]  Goldberg(4,4) dmccooeyDual Geodesic IcosahedraGoldberg 960 960 of 3 482 12 of 5,470 of 6 1440 dkt5dadkt5daD, cctI
Dual Geodesic Icosahedron Pattern 19 [7,0]  Goldberg(7,0) dmccooeyDual Geodesic IcosahedraGoldberg 980 980 of 3 492 12 of 5,480 of 6 1470
Dual Geodesic Icosahedron Pattern 2 [2,0]  Chamfered Dodecahedron, Goldberg(2,0) dmccooeyDual Geodesic IcosahedraGoldberg 80 80 of 3 42 30 of 6,12 of 5 120 cD
Dual Geodesic Icosahedron Pattern 20 [5,3]  Goldberg(5,3) dmccooeyDual Geodesic IcosahedraGoldberg 980 980 of 3 492 12 of 5,480 of 6 1470 wwD
Dual Geodesic Icosahedron Pattern 21 [6,2]  Goldberg(6,2) dmccooeyDual Geodesic IcosahedraGoldberg 1040 1040 of 3 522 12 of 5,510 of 6 1560
Dual Geodesic Icosahedron Pattern 22 [7,1]  Goldberg(7,1) dmccooeyDual Geodesic IcosahedraGoldberg 1140 1140 of 3 572 12 of 5,560 of 6 1710
Dual Geodesic Icosahedron Pattern 23 [5,4]  Goldberg(5,4) dmccooeyDual Geodesic IcosahedraGoldberg 1220 1220 of 3 612 12 of 5,600 of 6 1830
Dual Geodesic Icosahedron Pattern 24 [6,3]  Goldberg(6,3) dmccooeyDual Geodesic IcosahedraGoldberg 1260 1260 of 3 632 12 of 5,620 of 6 1890
Dual Geodesic Icosahedron Pattern 25 [8,0]  Goldberg(8,0) dmccooeyDual Geodesic IcosahedraGoldberg 1280 1280 of 3 642 12 of 5,630 of 6 1920 cccD
Dual Geodesic Icosahedron Pattern 3 [2,1]  Hexpropello Dodecahedron, Goldberg(2,1) dmccooeyDual Geodesic IcosahedraGoldberg 140 140 of 3 72 60 of 6,12 of 5 210 wD, dk5sD, t5gD
Dual Geodesic Icosahedron Pattern 4 [3,0]  Truncated Pentakis Dodecahedron, Goldberg(3,0) dmccooeyDual Geodesic IcosahedraGoldberg 180 180 of 3 92 80 of 6,12 of 5 270 tkD, dktI, tdtI
Dual Geodesic Icosahedron Pattern 5 [2,2]  Truncated Pentakis Icosidodecahedron, Goldberg(2,2) dmccooeyDual Geodesic IcosahedraGoldberg 240 240 of 3 122 110 of 6,12 of 5 360 ctI, dkt5daD
Dual Geodesic Icosahedron Pattern 6 [3,1]  Goldberg(3,1) dmccooeyDual Geodesic IcosahedraGoldberg 260 260 of 3 132 12 of 5,120 of 6 390
Dual Geodesic Icosahedron Pattern 7 [4,0]  Goldberg(4,0) dmccooeyDual Geodesic IcosahedraGoldberg 320 320 of 3 162 12 of 5,150 of 6 480 ccD
Dual Geodesic Icosahedron Pattern 8 [3,2]  Goldberg(3,2) dmccooeyDual Geodesic IcosahedraGoldberg 380 380 of 3 192 12 of 5,180 of 6 570
Dual Geodesic Icosahedron Pattern 9 [4,1]  Goldberg(4,1) dmccooeyDual Geodesic IcosahedraGoldberg 420 420 of 3 212 12 of 5,200 of 6 630 tk5sD
Dual Snub Hexpropello Dodecahedron (canonical)  dmccooeyDerived 632 560 of 3,60 of 6,12 of 5 420 420 of 5 1050 dswD
Dual Snub Truncated Icosahedron (canonical)  dmccooeyDerived 272 240 of 3,20 of 6,12 of 5 180 180 of 5 450 dstI
Dual Snub Truncated Octahedron (canonical)  dmccooeyDerived 110 6 of 4,96 of 3,8 of 6 72 72 of 5 180 dstO
Dürer's Solid  dmccooeyOther 12 12 of 3 8 6 of 5,2 of 3 18
Dürer's Solid revised  Other 12 12 of 3 8 6 of 5,2 of 3 18
eepT  Hart eeKpT
egD  CW designs egD
ekD  CW designs ekD
Elongated Dodecahedron  Space-filling 18 16 of 3,2 of 4 12 8 of 4,4 of 6 28
Elongated Square Gyrobicupola  dmccooeyOther 24 24 of 4 26 18 of 4,8 of 3 48
emD  CW designs emD
enneacontahedron  Hart jtD
eoD  CW designs eoD
epD  CW designs eKpD
Escher's Solid  dmccooeyconcaveOther 26 6 of 8,12 of 4,8 of 6 48 48 of 3 72 k(h=0.76)KjC
etD  CW designs etD
Excavated Dodecahedron  concavedeltahedron k(h=-0.25)D
Expanded Joined Hexpropello Dodecahedron (canonical)  dmccooeyDerived 840 840 of 4 842 60 of 6,12 of 5,630 of 4,140 of 3 1680 ejwD
Expanded Joined Truncated Pentakis Dodecahedron (canonical)  dmccooeyDerived 1080 1080 of 4 1082 80 of 6,12 of 5,810 of 4,180 of 3 2160 ejtkD
Expanded Propello Truncated Icosahedron (canonical)  dmccooeyDerived 900 900 of 4 902 20 of 6,12 of 5,810 of 4,60 of 3 1800 eptI
Geodesic Cube Pattern 1 [1,1]  Rhombic Dodecahedron dmccooeyGeodesic CubesSpace-filling 14 6 of 4,8 of 3 12 12 of 4 24 jC
Geodesic Cube Pattern 10 [3,3]  dmccooeyGeodesic Cubes 110 102 of 4,8 of 3 108 108 of 4 216
Geodesic Cube Pattern 11 [4,2]  dmccooeyGeodesic Cubes 122 114 of 4,8 of 3 120 120 of 4 240 oKpC
Geodesic Cube Pattern 12 [5,0]  dmccooeyGeodesic Cubes 152 144 of 4,8 of 3 150 150 of 4 300 pKpC
Geodesic Cube Pattern 13 [4,3]  dmccooeyGeodesic Cubes 152 144 of 4,8 of 3 150 150 of 4 300
Geodesic Cube Pattern 14 [5,1]  dmccooeyGeodesic Cubes 158 150 of 4,8 of 3 156 156 of 4 312
Geodesic Cube Pattern 15 [5,2]  dmccooeyGeodesic Cubes 176 168 of 4,8 of 3 174 174 of 4 348
Geodesic Cube Pattern 16[4,4]  Geodesic Cubes 194 192 192 of 4 384 oojC
Geodesic Cube Pattern 2 [2,0]  Deltoidal Icositetrahedron dmccooeyGeodesic Cubes 26 18 of 4,8 of 3 24 24 of 4 48 oC
Geodesic Cube Pattern 3 [2,1]  Propello Cube dmccooeyGeodesic Cubes 32 24 of 4,8 of 3 30 30 of 4 60 pC
Geodesic Cube Pattern 4 [2,2]  dmccooeyGeodesic Cubes 50 42 of 4,8 of 3 48 48 of 4 96 ojC
Geodesic Cube Pattern 5 [3,0]  dmccooeyGeodesic Cubes 56 48 of 4,8 of 3 54 54 of 4 108
Geodesic Cube Pattern 6 [3,1]  dmccooeyGeodesic Cubes 62 54 of 4,8 of 3 60 60 of 4 120 jKpC
Geodesic Cube Pattern 7 [3,2]  dmccooeyGeodesic Cubes 80 72 of 4,8 of 3 78 78 of 4 156
Geodesic Cube Pattern 8 [4,0]  dmccooeyGeodesic Cubes 98 90 of 4,8 of 3 96 96 of 4 192 ooC
Geodesic Cube Pattern 9 [4,1]  dmccooeyGeodesic Cubes 104 96 of 4,8 of 3 102 102 of 4 204
Geodesic Icosahedron Pattern 1 [1,1]  Pentakis Dodecahedron dmccooeyGeodesic Icosahedra 32 20 of 6,12 of 5 60 60 of 3 90 kI, kD
Geodesic Icosahedron Pattern 10 [5,0]  dmccooeyGeodesic Icosahedra 252 240 of 6,12 of 5 500 500 of 3 750
Geodesic Icosahedron Pattern 11 [3,3]  dmccooeyGeodesic Icosahedra 272 260 of 6,12 of 5 540 540 of 3 810
Geodesic Icosahedron Pattern 12 [4,2]  dmccooeyGeodesic Icosahedra 282 270 of 6,12 of 5 560 560 of 3 840
Geodesic Icosahedron Pattern 13 [5,1]  dmccooeyGeodesic Icosahedra 312 300 of 6,12 of 5 620 620 of 3 930
Geodesic Icosahedron Pattern 14 [6,0]  dmccooeyGeodesic Icosahedra 362 350 of 6,12 of 5 720 720 of 3 1080
Geodesic Icosahedron Pattern 15 [4,3]  dmccooeyGeodesic Icosahedra 372 360 of 6,12 of 5 740 740 of 3 1110
Geodesic Icosahedron Pattern 16 [5,2]  dmccooeyGeodesic Icosahedra 392 380 of 6,12 of 5 780 780 of 3 1170
Geodesic Icosahedron Pattern 17 [6,1]  dmccooeyGeodesic Icosahedra 432 420 of 6,12 of 5 860 860 of 3 1290
Geodesic Icosahedron Pattern 18 [4,4]  dmccooeyGeodesic Icosahedra 482 470 of 6,12 of 5 960 960 of 3 1440
Geodesic Icosahedron Pattern 19 [7,0]  dmccooeyGeodesic Icosahedra 492 480 of 6,12 of 5 980 980 of 3 1470
Geodesic Icosahedron Pattern 2 [2,0]  Pentakis Icosidodecahedron dmccooeyGeodesic Icosahedra 42 30 of 6,12 of 5 80 80 of 3 120 vI, k5aD
Geodesic Icosahedron Pattern 20 [5,3]  dmccooeyGeodesic Icosahedra 492 480 of 6,12 of 5 980 980 of 3 1470
Geodesic Icosahedron Pattern 21 [6,2]  dmccooeyGeodesic Icosahedra 522 510 of 6,12 of 5 1040 1040 of 3 1560
Geodesic Icosahedron Pattern 22 [7,1]  dmccooeyGeodesic Icosahedra 572 560 of 6,12 of 5 1140 1140 of 3 1710
Geodesic Icosahedron Pattern 23 [5,4]  dmccooeyGeodesic Icosahedra 612 600 of 6,12 of 5 1220 1220 of 3 1830
Geodesic Icosahedron Pattern 24 [6,3]  dmccooeyGeodesic Icosahedra 632 620 of 6,12 of 5 1260 1260 of 3 1890
Geodesic Icosahedron Pattern 25 [8,0]  dmccooeyGeodesic Icosahedra 642 630 of 6,12 of 5 1280 1280 of 3 1920
Geodesic Icosahedron Pattern 3 [2,1]  Pentakis Snub Dodecahedron dmccooeyGeodesic Icosahedra 72 60 of 6,12 of 5 140 140 of 3 210 k5sD
Geodesic Icosahedron Pattern 4 [3,0]  Hexakis-Pentakis Truncated Icosahedron dmccooeyGeodesic Icosahedra 92 80 of 6,12 of 5 180 180 of 3 270
Geodesic Icosahedron Pattern 5 [2,2]  Hexakis-Pentakis Chamfered Dodecahedron dmccooeyGeodesic Icosahedra 122 110 of 6,12 of 5 240 240 of 3 360
Geodesic Icosahedron Pattern 6 [3,1]  dmccooeyGeodesic Icosahedra 132 120 of 6,12 of 5 260 260 of 3 390
Geodesic Icosahedron Pattern 7 [4,0]  dmccooeyGeodesic Icosahedra 162 150 of 6,12 of 5 320 320 of 3 480
Geodesic Icosahedron Pattern 8 [3,2]  dmccooeyGeodesic Icosahedra 192 180 of 6,12 of 5 380 380 of 3 570
Geodesic Icosahedron Pattern 9 [4,1]  dmccooeyGeodesic Icosahedra 212 200 of 6,12 of 5 420 420 of 3 630
gmD  CW designs gmD
Great Cubicuboctahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 24 24 of 4 20 6 of 8,6 of 4,8 of 3 42
Great Deltoidal Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 62 30 of 4,20 of 3,12 of 5 60 60 of 4 120
Great Deltoidal Icositetrahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 26 18 of 4,8 of 3 24 24 of 4 48
Great Dirhombicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 8 124 24 of 5,60 of 4,40 of 3 182
Great Disdyakis Dodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 26 6 of 8,12 of 4,8 of 6 48 48 of 3 72
Great Disdyakis Triacontahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 62 30 of 4,20 of 6,12 of 10 120 120 of 3 180
Great Ditrigonal Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12 of 10,20 of 3,12 of 5 60 60 of 4 102
Great Ditrigonal Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 44 12 of 10,12 of 5,20 of 3 102
Great Ditrigonal Icosidodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 20 20 of 6 32 12 of 5,20 of 3 50
Great Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12 of 10,20 of 3,12 of 5 60 60 of 4 102
Great Dodecahedron  dmccooeyKepler-Poinsotconcave 12 12 of 5 12 12 of 5 22 k(h=-0.2)I
Great Dodecahemicosahedron  dmccooeyVersi-Regularconcave 30 30 of 4 22 10 of 6,12 of 5 50
Great Dodecahemidodecahedron  dmccooeyVersi-Regularconcave 30 30 of 4 18 6 of 10,12 of 5 46
Great Dodecicosacron  dmccooeyVersi-Quasi-Regular Dualsconcave 32 12 of 10,20 of 6 60 60 of 4 90
Great Dodecicosahedron  dmccooeyVersi-Quasi-Regularconcave 60 60 of 4 32 12 of 10,20 of 6 90
Great Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 44 12 of 10,12 of 5,20 of 3 102
Great Hexacronic Icositetrahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 20 6 of 8,6 of 4,8 of 3 24 24 of 4 42
Great Hexagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 104 80 of 3,24 of 5 60 60 of 6 162
Great Icosacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 52 20 of 6,12 of 5,20 of 3 60 60 of 4 110
Great Icosahedron  dmccooeyKepler-Poinsotconcave 12 12 of 5 20 20 of 3 30 k(h=-0.2)k(h=1)D
Great Icosicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 52 20 of 6,12 of 5,20 of 3 110
Great Icosidodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 30 30 of 4 32 12 of 5,20 of 3 60
Great Icosihemidodecahedron  dmccooeyVersi-Regularconcave 30 30 of 4 26 6 of 10,20 of 3 54
Great Inverted pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 92 80 of 3,12 of 5 60 60 of 5 150
Great Inverted Snub Icosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 5 92 12 of 5,80 of 3 150
Great pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 92 80 of 3,12 of 5 60 60 of 5 150
Great pentagrammic Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 92 80 of 3,12 of 5 60 60 of 5 150
Great Pentakis Dodecahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 24 12 of 10,12 of 5 60 60 of 3 82
Great Retrosnub Icosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 5 92 12 of 5,80 of 3 150
Great Rhombic Triacontahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 32 12 of 5,20 of 3 30 30 of 4 60
Great Rhombidodecacron  dmccooeyVersi-Quasi-Regular Dualsconcave 42 12 of 10,30 of 4 60 60 of 4 100
Great Rhombidodecahedron  dmccooeyVersi-Quasi-Regularconcave 60 60 of 4 42 12 of 10,30 of 4 100
Great Rhombihexacron  dmccooeyVersi-Quasi-Regular Dualsconcave 18 6 of 8,12 of 4 24 24 of 4 40
Great Rhombihexahedron  dmccooeyVersi-Quasi-Regularconcave 24 24 of 4 18 6 of 8,12 of 4 40
Great Snub Dodecicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 6 104 24 of 5,80 of 3 162
Great Snub Icosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 5 92 12 of 5,80 of 3 150
Great Stellapentakis Dodecahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 32 20 of 6,12 of 5 60 60 of 3 90
Great Stellated Dodecahedron  Stellated Great Dodecahedron dmccooeyKepler-Poinsotconcave 20 20 of 3 12 12 of 5 30 k(h=1.6)I
Great Stellated Truncated Dodecahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60 of 3 32 12 of 10,20 of 3 90
Great Triakis Icosahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 32 12 of 10,20 of 3 60 60 of 3 90
Great Triakis Octahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 14 6 of 8,8 of 3 24 24 of 3 36
Great Triambic Icosahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 32 20 of 3,12 of 5 20 20 of 6 50
Great Truncated Cuboctahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 48 48 of 3 26 6 of 8,8 of 6,12 of 4 72
Great Truncated Icosidodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 120 120 of 3 62 12 of 10,20 of 6,30 of 4 180
Gyrate Deltoidal Icositetrahedron  dmccooeyOther 26 18 of 4,8 of 3 24 24 of 4 48
gyrogyrocube  Hart ggC
Heptagonal Antiprism  dmccooeyAntiprisms 14 14 of 4 16 2 of 7,14 of 3 28 A7
Heptagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 9 2 of 7,7 of 4 14 14 of 3 21 dP7
Heptagonal Dodecahedron (type A) (C3-symmetric form 3)  dmccooeyHigher Genus Toroidalconcave 28 28 of 3 12 12 of 7 38
Heptagonal Dodecahedron (type A) (S4-symmetric form 1)  dmccooeyHigher Genus Toroidalconcave 28 28 of 3 12 12 of 7 38
Heptagonal Dodecahedron (type B) (form 1)  dmccooeyHigher Genus Toroidalconcave 28 28 of 3 12 12 of 7 38
Heptagonal Dodecahedron (type C) (form 1)  dmccooeyHigher Genus Toroidalconcave 28 28 of 3 12 12 of 7 38
Heptagonal Dodecahedron (type D) (form 3)  dmccooeyHigher Genus Toroidalconcave 28 28 of 3 12 12 of 7 38
Heptagonal Dodecahedron (type E) (form 1)  dmccooeyHigher Genus Toroidalconcave 28 28 of 3 12 12 of 7 38
Heptagonal Iris Toroid  dmccooeyNon-Regular Toroidalconcave 14 14 of 5 21 7 of 4,14 of 3 33
Heptagonal Prism  dmccooeyPrisms 14 14 of 3 9 2 of 7,7 of 4 21 P7
Heptagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 16 2 of 7,14 of 3 14 14 of 4 28 dA7
Heptagrammic 7/2 Antiprism  dmccooeyStar Prisms and Antiprismsconcave 14 14 of 4 16 2 of 7,14 of 3 28
Heptagrammic 7/2 Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 9 2 of 7,7 of 4 14 14 of 3 21
Heptagrammic 7/2 Prism  dmccooeyStar Prisms and Antiprismsconcave 14 14 of 3 9 2 of 7,7 of 4 21
Heptagrammic 7/2 Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 16 2 of 7,14 of 3 14 14 of 4 28
Heptagrammic 7/3 Antiprism  dmccooeyStar Prisms and Antiprismsconcave 14 14 of 4 16 2 of 7,14 of 3 28
Heptagrammic 7/3 Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 9 2 of 7,7 of 4 14 14 of 3 21
Heptagrammic 7/3 Prism  dmccooeyStar Prisms and Antiprismsconcave 14 14 of 3 9 2 of 7,7 of 4 21
Heptagrammic 7/3 Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 16 2 of 7,14 of 3 14 14 of 4 28
Heptagrammic Concave Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 16 2 of 7,14 of 3 14 14 of 4 28
Heptagrammic Crossed Antiprism  dmccooeyStar Prisms and Antiprismsconcave 14 14 of 4 16 2 of 7,14 of 3 28
Hexagonal Antiprism  dmccooeyAntiprisms 12 12 of 4 14 2 of 6,12 of 3 24 A6
Hexagonal Antiprism-Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 24 12 of 5,12 of 3 24 12 of 5,12 of 3 46
Hexagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 8 2 of 6,6 of 4 12 12 of 3 18 dP6
Hexagonal Prism  dmccooeyPrismsSpace-filling 12 12 of 3 8 2 of 6,6 of 4 18 P6
Hexagonal Toroid with 8 overarching faces  dmccooeyRegular Hexagonal Toroidalconcave 16 16 of 3 8 8 of 6 22
Hexagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 14 2 of 6,12 of 3 12 12 of 4 24 dA6
Hexagonal Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 36 12 of 4,24 of 3 24 24 of 5 58
Hexagonal Trapezohedron-Antiprism Toroid  dmccooeyNon-Regular Toroidalconcave 24 12 of 5,12 of 3 24 12 of 5,12 of 3 46
Hexpropello Cube (dextro) (canonical)  dmccooeyDerived 56 56 of 3 30 24 of 6,6 of 4 84 wC
Hexpropello Dodecahedron (dextro) (canonical)  dmccooeyDerived 140 140 of 3 72 60 of 6,12 of 5 210 wD
Hugel's Polyhedron  concavedmccooeyOther 20 20 of 6 20 20 of 6 38 i(r=0.2,h=-0.5)D
Icosahedron  dmccooeyPlatonicisohedrondeltahedronGeodesic Icosahedra 12 12 of 5 20 20 of 3 30 I, sY3, k5aY5
Icosidodecadodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 44 20 of 6,24 of 5 102
Icosidodecahedron  dmccooeyArchimedean 30 30 of 4 32 12 of 5,20 of 3 60 aD
Icositruncated Dodecadodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 120 120 of 3 44 24 of 10,20 of 6 162
Inverted Snub Dodecadodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 5 84 24 of 5,60 of 3 142
Isohedral Toroid with 24 faces  dmccooeyNon-Regular Toroidalconcave 12 6 of 7,6 of 5 24 24 of 3 34
J1  Square Pyramid(J1) JohnsonPyramids 5 4 of 3,1 of 4 5 4 of 3,1 of 4 8 Y4
J10  Gyroelongated Square Pyramid Johnson 9 4 of 5,5 of 4 13 12 of 3,1 of 4 20
J11  Gyroelongated pentagonal Pyramid Johnson 11 5 of 4,6 of 5 16 15 of 3,1 of 5 25
J12  Triangular Dipyramid Johnsondeltahedron 5 3 of 4,2 of 3 6 6 of 3 9
J13  pentagonal Dipyramid Johnsondeltahedron 7 5 of 4,2 of 5 10 10 of 3 15
J14  Elongated Triangular Dipyramid Johnson 8 6 of 4,2 of 3 9 6 of 3,3 of 4 15
J15  Elongated Square Dipyramid Johnson 10 10 of 4 12 8 of 3,4 of 4 20
J16  Elongated pentagonal Dipyramid Johnson 12 10 of 4,2 of 5 15 10 of 3,5 of 4 25
J17  Gyroelongated Square Dipyramid Johnsondeltahedron 10 8 of 5,2 of 4 16 16 of 3 24
J18  Elongated Triangular Cupola Johnson 15 9 of 4,6 of 3 14 4 of 3,9 of 4,1 of 6 27
J19  Elongated Square Cupola Johnson 20 12 of 4,8 of 3 18 4 of 3,13 of 4,1 of 8 36
J2  pentagonal Pyramid(J2) JohnsonPyramids 6 5 of 3,1 of 5 6 5 of 3,1 of 5 10 Y5
J20  Elongated pentagonal Cupola Johnson 25 15 of 4,10 of 3 22 5 of 3,15 of 4,1 of 5,1 of 10 45
J21  Elongated pentagonal Rotunda Johnson 30 20 of 4,10 of 3 27 10 of 3,10 of 4,6 of 5,1 of 10 55
J22  Gyroelongated Triangular Cupola Johnson 15 6 of 5,9 of 4 20 16 of 3,3 of 4,1 of 6 33
J23  Gyroelongated Square Cupola Johnson 20 12 of 4,8 of 5 26 20 of 3,5 of 4,1 of 8 44
J24  Gyroelongated pentagonal Cupola Johnson 25 15 of 4,10 of 5 32 25 of 3,5 of 4,1 of 5,1 of 10 55
J25  Gyroelongated pentagonal Rotunda Johnson 30 10 of 5,20 of 4 37 30 of 3,6 of 5,1 of 10 65
J26  Gyrobifastigium JohnsonSpace-filling 8 4 of 4,4 of 3 8 4 of 3,4 of 4 14
J27  Triangular Orthobicupola Johnson 12 12 of 4 14 8 of 3,6 of 4 24
J28  Square Orthobicupola Johnson 16 16 of 4 18 8 of 3,10 of 4 32
J29  Square Gyrobicupola Johnson 16 16 of 4 18 8 of 3,10 of 4 32
J3  Triangular Cupola(J3) Johnson 9 6 of 3,3 of 4 8 4 of 3,3 of 4,1 of 6 15
J30  pentagonal Orthobicupola Johnson 20 20 of 4 22 10 of 3,10 of 4,2 of 5 40
J31  pentagonal Gyrobicupola Johnson 20 20 of 4 22 10 of 3,10 of 4,2 of 5 40
J32  pentagonal Orthocupolarontunda Johnson 25 25 of 4 27 15 of 3,5 of 4,7 of 5 50
J33  pentagonal Gyrocupolarotunda Johnson 25 25 of 4 27 15 of 3,5 of 4,7 of 5 50
J34  pentagonal Orthobirotunda Johnson 30 30 of 4 32 20 of 3,12 of 5 60
J35  Elongated Triangular Orthobicupola Johnson 18 18 of 4 20 8 of 3,12 of 4 36
J36  Elongated Triangular Gyrobicupola Johnson 18 18 of 4 20 8 of 3,12 of 4 36
J37  Elongated Square Gyrobicupola, Pseudorhombicuboctahedron, Miller's Solid Johnson 24 24 of 4 26 8 of 3,18 of 4 48
J38  Elongated pentagonal Orthobicupola Johnson 30 30 of 4 32 10 of 3,20 of 4,2 of 5 60
J39  Elongated pentagonal Gyrobicupola Johnson 30 30 of 4 32 10 of 3,20 of 4,2 of 5 60
J4  Square Cupola(J4) Johnson 12 8 of 3,4 of 4 10 4 of 3,5 of 4,1 of 8 20
J40  Elongated pentagonal Orthocupolarotunda Johnson 35 35 of 4 37 15 of 3,15 of 4,7 of 5 70
J41  Elongated pentagonal Gyrocupolarotunda Johnson 35 35 of 4 37 15 of 3,15 of 4,7 of 5 70
J42  Elongated pentagonal Orthobirotunda Johnson 40 40 of 4 42 20 of 3,10 of 4,12 of 5 80
J43  Elongated pentagonal Gyrobirotunda Johnson 40 40 of 4 42 20 of 3,10 of 4,12 of 5 80
J44  Gyroelongated Triangular Bicupola Johnson 18 12 of 5,6 of 4 26 20 of 3,6 of 4 42
J45  Gyroelongated Square Bicupola Johnson 24 16 of 5,8 of 4 34 24 of 3,10 of 4 56
J46  Gyroelongated pentagonal Bicupola Johnson 30 20 of 5,10 of 4 42 30 of 3,10 of 4,2 of 5 70
J47  Gyroelongated pentagonal Cupolarotunda Johnson 35 20 of 5,15 of 4 47 35 of 3,5 of 4,7 of 5 80
J48  Gyroelongated pentagonal Birotunda Johnson 40 20 of 4,20 of 5 52 40 of 3,12 of 5 90
J49  Augmented Triangular Prism Johnson 7 5 of 4,2 of 3 8 6 of 3,2 of 4 13
J5  pentagonal Cupola(J5) Johnson 15 10 of 3,5 of 4 12 5 of 3,5 of 4,1 of 5,1 of 10 25
J50  Biaugmented Triangular Prism Johnson 8 6 of 4,2 of 5 11 10 of 3,1 of 4 17
J51  Triaugmented Triangular Prism Johnsondeltahedron 9 6 of 5,3 of 4 14 14 of 3 21
J52  Augmented pentagonal Prism Johnson 11 6 of 3,5 of 4 10 4 of 3,4 of 4,2 of 5 19
J53  Biaugmented pentagonal Prism Johnson 12 10 of 4,2 of 3 13 8 of 3,3 of 4,2 of 5 23
J54  Augmented Hexagonal Prism Johnson 13 8 of 3,5 of 4 11 4 of 3,5 of 4,2 of 6 22
J55  Parabiaugmented Hexagonal Prism Johnson 14 10 of 4,4 of 3 14 8 of 3,4 of 4,2 of 6 26
J56  Metabiaugmented Hexagonal Prism Johnson 14 10 of 4,4 of 3 14 8 of 3,4 of 4,2 of 6 26
J57  Triaugmented Hexagonal Prism Johnson 15 15 of 4 17 12 of 3,3 of 4,2 of 6 30
J58  Augmented Dodecahedron Johnson 21 5 of 4,1 of 5,15 of 3 16 5 of 3,11 of 5 35
J59  Parabiaugmented Dodecahedron Johnson 22 2 of 5,10 of 4,10 of 3 20 10 of 3,10 of 5 40
J6  pentagonal Rotunda(J6) Johnson 20 10 of 3,10 of 4 17 10 of 3,6 of 5,1 of 10 35
J60  Metabiaugmented Dodecahedron Johnson 22 10 of 3,10 of 4,2 of 5 20 10 of 3,10 of 5 40
J61  Triaugmented Dodecahedron Johnson 23 15 of 4,3 of 5,5 of 3 24 15 of 3,9 of 5 45
J62  Metabidiminished Icosahedron Johnson 10 2 of 5,6 of 4,2 of 3 12 10 of 3,2 of 5 20
J63  Tridiminished Icosahedron Johnson 9 3 of 4,6 of 3 8 5 of 3,3 of 5 15
J64  Augmented Tridiminished Icosahedron Johnson 10 6 of 4,4 of 3 10 7 of 3,3 of 5 18
J65  Augmented Truncated Tetrahedron Johnson 15 6 of 3,9 of 4 14 8 of 3,3 of 4,3 of 6 27
J66  Augmented Truncated Cube Johnson 28 16 of 3,12 of 4 22 12 of 3,5 of 4,5 of 8 48
J67  Biaugmented Truncated Cube Johnson 32 24 of 4,8 of 3 30 16 of 3,10 of 4,4 of 8 60
J68  Augmented Truncated Dodecahedron Johnson 65 50 of 3,15 of 4 42 25 of 3,5 of 4,1 of 5,11 of 10 105
J69  Parabiaugmented Truncated Dodecahedron Johnson 70 40 of 3,30 of 4 52 30 of 3,10 of 4,2 of 5,10 of 10 120
J7  Elongated Triangular Pyramid(J7) Johnson 7 4 of 3,3 of 4 7 4 of 3,3 of 4 12
J70  Metabiaugmented Truncated Dodecahedron Johnson 70 30 of 4,40 of 3 52 30 of 3,10 of 4,2 of 5,10 of 10 120
J71  Triaugmented Truncated Dodecahedron Johnson 75 30 of 3,45 of 4 62 35 of 3,15 of 4,3 of 5,9 of 10 135
J72  Gyrate Rhombicosidodecahedron Johnson 60 60 of 4 62 20 of 3,30 of 4,12 of 5 120
J73  Parabigyrate Rhombicosidodecahedron Johnson 60 60 of 4 62 20 of 3,30 of 4,12 of 5 120
J74  Metabigyrate Rhombicosidodecahedron Johnson 60 60 of 4 62 20 of 3,30 of 4,12 of 5 120
J75  Trigyrate Rhombicosidodecahedron Johnson 60 60 of 4 62 20 of 3,30 of 4,12 of 5 120
J76  Diminished Rhombicosidodecahedron Johnson 55 45 of 4,10 of 3 52 15 of 3,25 of 4,11 of 5,1 of 10 105
J77  Paragyrate Diminished Rhombicosidodecahedron Johnson 55 45 of 4,10 of 3 52 15 of 3,25 of 4,11 of 5,1 of 10 105
J78  Metagyrate Diminished Rhombicosidodecahedron Johnson 55 45 of 4,10 of 3 52 15 of 3,25 of 4,11 of 5,1 of 10 105
J79  Bigyrate Diminished Rhombicosidodecahedron Johnson 55 10 of 3,45 of 4 52 15 of 3,25 of 4,11 of 5,1 of 10 105
J8  Elongated Square Pyramid(J8) Johnson 9 4 of 3,5 of 4 9 4 of 3,5 of 4 16
J80  Parabidiminished Rhombicosidodecahedron Johnson 50 20 of 3,30 of 4 42 10 of 3,20 of 4,10 of 5,2 of 10 90
J81  Metabidiminished Rhombicosidodecahedron Johnson 50 30 of 4,20 of 3 42 10 of 3,20 of 4,10 of 5,2 of 10 90
J82  Gyrate Bidiminished Rhombicosidodecahedron Johnson 50 30 of 4,20 of 3 42 10 of 3,20 of 4,10 of 5,2 of 10 90
J83  Tridiminished Rhombicosidodecahedron Johnson 45 15 of 4,30 of 3 32 5 of 3,15 of 4,9 of 5,3 of 10 75
J84  Snub Disphenoid Johnsondeltahedron 8 4 of 4,4 of 5 12 12 of 3 18
J85  Snub Square Antiprism Johnson 16 16 of 5 26 24 of 3,2 of 4 40
J86  Sphenocorona Johnson 10 6 of 4,4 of 5 14 12 of 3,2 of 4 22
J87  Augmented Sphenocorona Johnson 11 3 of 4,8 of 5 17 16 of 3,1 of 4 26
J88  Sphenomegacorona Johnson 12 8 of 5,4 of 4 18 16 of 3,2 of 4 28
J89  Hebesphenomegacorona Johnson 14 10 of 5,4 of 4 21 18 of 3,3 of 4 33
J9  Elongated pentagonal Pyramid(J9) Johnson 11 5 of 3,5 of 4,1 of 5 11 5 of 3,5 of 4,1 of 5 20
J90  Disphenocingulum Johnson 16 4 of 4,12 of 5 24 20 of 3,4 of 4 38
J91  Bilunabirotunda Johnson 14 10 of 4,4 of 3 14 8 of 3,2 of 4,4 of 5 26
J92  Triangular Hebesphenorotunda Johnson 18 18 of 4 20 13 of 3,3 of 4,3 of 5,1 of 6 36
Jessen's Orthogonal Icosahedron  dmccooeyconcaveOther 12 12 of 5 20 20 of 3 30
Joined Cuboctahedron  dmccooeyArchimedean-Catalan Hulls 26 18 of 4,8 of 3 24 24 of 4 48 jaC
Joined Icosidodecahedron  dmccooeyArchimedean-Catalan Hulls 62 30 of 4,20 of 3,12 of 5 60 60 of 4 120 jI
Joined Rhombicosidodecahedron  dmccooeyArchimedean-Catalan Hulls 122 90 of 4,20 of 3,12 of 5 120 120 of 4 240 jeD
Joined Rhombicuboctahedron  dmccooeyArchimedean-Catalan Hulls 50 42 of 4,8 of 3 48 48 of 4 96 jeO
Joined Snub Cube (dextro)  dmccooeyArchimedean-Catalan Hulls 62 6 of 4,24 of 5,32 of 3 60 60 of 4 120 rjsC
Joined Snub Cube (laevo)  dmccooeyArchimedean-Catalan Hulls 62 6 of 4,24 of 5,32 of 3 60 60 of 4 120 jsC
Joined Snub Dodecahedron (dextro)  dmccooeyArchimedean-Catalan Hulls 152 72 of 5,80 of 3 150 150 of 4 300 rjsD
Joined Snub Dodecahedron (laevo)  dmccooeyArchimedean-Catalan Hulls 152 72 of 5,80 of 3 150 150 of 4 300 jsD
Joined Truncated Cube  dmccooeyArchimedean-Catalan Hulls 38 6 of 8,32 of 3 36 36 of 4 72 jtC
Joined Truncated Cuboctahedron  dmccooeyArchimedean-Catalan Hulls 74 6 of 8,48 of 3,12 of 4,8 of 6 72 72 of 4 144 jaD
Joined Truncated Dodecahedron  dmccooeyArchimedean-Catalan Hulls 92 12 of 10,80 of 3 90 90 of 4 180 jtD
Joined Truncated Icosahedron  dmccooeyArchimedean-Catalan Hulls 92 20 of 6,60 of 3,12 of 5 90 90 of 4 180 jtI
Joined Truncated Icosidodecahedron  dmccooeyArchimedean-Catalan Hulls 182 30 of 4,120 of 3,20 of 6,12 of 10 180 180 of 4 360 jteD
Joined Truncated Octahedron  dmccooeyArchimedean-Catalan HullsSpace-filling 38 6 of 4,24 of 3,8 of 6 36 36 of 4 72 jtO
Joined Truncated Tetrahedron  dmccooeyArchimedean-Catalan Hulls 20 4 of 6,16 of 3 18 18 of 4 36 jtT
jP3  Hart 0 9 9 of 4 7 NKjP3
k12dk12dk12dk12P12  Hart k12dk12dk12dk12P12
Klein Map Dual {3,7}8 (Schulte & Wills)  dmccooeyHigher Genus Toroidalconcave 24 24 of 7 56 56 of 3 78
Klein Map {7,3}8 (basic shape)  dmccooeyHigher Genus Toroidalconcave 56 56 of 3 24 24 of 7 78
Knotted Dodecahedron  dmccooeyNon-Regular Toroidalconcave 18 12 of 3,6 of 4 12 6 of 4,6 of 6 28
L-Propello L-Snub Cube (canonical)  dmccooeyPropellor 144 120 of 4,24 of 5 158 126 of 4,32 of 3 300 pdtO
L-Propello R-pentagonal Icositetrahedron (canonical)  dmccooeyPropellor 158 126 of 4,32 of 3 144 24 of 5,120 of 4 300 pgC
meD  CW designs meD
Medial Deltoidal Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 54 30 of 4,24 of 5 60 60 of 4 112
Medial Disdyakis Triacontahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 54 24 of 10,30 of 4 120 120 of 3 172
Medial Hexagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 104 24 of 5,80 of 3 60 60 of 6 162
Medial Icosacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 20 of 6,24 of 5 60 60 of 4 102
Medial Inverted pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 84 24 of 5,60 of 3 60 60 of 5 142
Medial pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 84 24 of 5,60 of 3 60 60 of 5 142
Medial Rhombic Triacontahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 24 24 of 5 30 30 of 4 52
Medial Triambic Icosahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 24 24 of 5 20 20 of 6 42
Octagonal Antiprism  dmccooeyAntiprisms 16 16 of 4 18 2 of 8,16 of 3 32 A8
Octagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 10 2 of 8,8 of 4 16 16 of 3 24 dP8
Octagonal Iris Toroid  dmccooeyNon-Regular Toroidalconcave 16 16 of 5 24 8 of 4,16 of 3 38
Octagonal Prism  dmccooeyPrisms 16 16 of 3 10 2 of 8,8 of 4 24 P8
Octagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 18 2 of 8,16 of 3 16 16 of 4 32 dA8
Octagrammic Antiprism  dmccooeyStar Prisms and Antiprismsconcave 16 16 of 4 18 2 of 8,16 of 3 32
Octagrammic Concave Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 18 2 of 8,16 of 3 16 16 of 4 32
Octagrammic Crossed Antiprism  dmccooeyStar Prisms and Antiprismsconcave 16 16 of 4 18 2 of 8,16 of 3 32
Octagrammic Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 10 2 of 8,8 of 4 16 16 of 3 24
Octagrammic Prism  dmccooeyStar Prisms and Antiprismsconcave 16 16 of 3 10 2 of 8,8 of 4 24
Octagrammic Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 18 2 of 8,16 of 3 16 16 of 4 32
Octahedron  Square Dipyramid dmccooeyPlatonicisohedrondeltahedron 6 6 of 4 8 8 of 3 12 O, aY3
Octahemioctahedron  dmccooeyVersi-Regularconcave 12 12 of 4 12 4 of 6,8 of 3 22 k(h=-0.7,fn=[4])aC
Orthokis Propello Cube (canonical)  dmccooeyDerived 38 6 of 4,24 of 5,8 of 3 48 24 of 4,24 of 3 84 k(regular=true)pC
Orthokis Propello Dodecahedron (canonical)  dmccooeyDerived 92 72 of 5,20 of 3 120 60 of 4,60 of 3 210 k(regular=true)pD
Orthotruncated Propello Icosahedron (canonical)  dmccooeyDerived 120 60 of 4,60 of 3 92 72 of 5,20 of 3 210
Orthotruncated Propello Octahedron (canonical)  dmccooeyDerived 48 24 of 3,24 of 4 38 24 of 5,6 of 4,8 of 3 84
pentagonal Antiprism  dmccooeyAntiprisms 10 12 10 of 3,2 of 5 20 A5
pentagonal Antiprism-Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 20 10 of 5,10 of 3 20 10 of 5,10 of 3 38
pentagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 7 2 of 5,5 of 4 10 10 of 3 15 dP5
pentagonal Hexecontahedron  dmccooeyCatalanchiralisohedron 92 80 of 3,12 of 5 60 60 of 5 150 gD
pentagonal Icositetrahedron  gyroid dmccooeychiralCatalanisohedron 38 6 of 4,32 of 3 24 24 of 5 60 gC
pentagonal Prism  dmccooeyPrisms 10 10 of 3 7 2 of 5,5 of 4 15 P5
Pentagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 12 10 of 3,2 of 5 10 10 of 4 20 dA5
pentagonal Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 30 20 of 3,10 of 4 20 20 of 5 48
pentagonal Trapezohedron-Antiprism Toroid  dmccooeyNon-Regular Toroidalconcave 20 20 10 of 3,10 of 5 38
Pentagrammic Antiprism  dmccooeyStar Prisms and Antiprismsconcave 10 10 of 4 12 2 of 5,10 of 3 20
pentagrammic Concave Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 12 10 of 3,2 of 5 10 10 of 4 20
Pentagrammic Crossed Antiprism  dmccooeyStar Prisms and Antiprismsconcave 10 10 of 4 12 2 of 5,10 of 3 20
Pentagrammic Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 7 2 of 5,5 of 4 10 10 of 3 15
Pentagrammic Prism  dmccooeyStar Prisms and Antiprismsconcave 10 10 of 3 7 2 of 5,5 of 4 15
pentagrammic Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 12 10 of 3,2 of 5 10 10 of 4 20
Pentakis Dodecahedron  dmccooeyCatalanisohedronGeodesic Icosahedra 32 20 of 6,12 of 5 60 60 of 3 90 kD
Pentakis Icosidodecahedron (canonical)  dmccooeyDerivedGeodesic Icosahedra 42 30 of 6,12 of 5 80 80 of 3 120
Pentakis Snub Dodecahedron (laevo) (canonical)  dmccooeyDerived 72 60 of 6,12 of 5 140 140 of 3 210
poI  CW designs poI
Propello Cube (canonical)  dmccooeyPropellor 32 24 of 4,8 of 3 30 30 of 4 60 pC
Propello Disdyakis Dodecahedron (canonical)  dmccooeyPropellor 170 6 of 8,156 of 4,8 of 6 192 144 of 4,48 of 3 360 pmC
Propello Disdyakis Triacontahedron (canonical)  dmccooeyPropellor 422 390 of 4,20 of 6,12 of 10 480 360 of 4,120 of 3 900 pmD
Propello Dodecahedron (canonical)  dmccooeyPropellor 80 60 of 4,20 of 3 72 12 of 5,60 of 4 150 pD
Propello Icosahedron (canonical)  dmccooeyPropellor 72 60 of 4,12 of 5 80 60 of 4,20 of 3 150 pI
Propello Octahedron (canonical)  dmccooeyPropellor 30 30 of 4 32 24 of 4,8 of 3 60 pO
Propello Pentakis Dodecahedron (canonical)  dmccooeyPropellor 212 180 of 4,20 of 6,12 of 5 240 180 of 4,60 of 3 450 pkD
Propello Tetrahedron (canonical)  dmccooeyPropellor 16 12 of 4,4 of 3 16 12 of 4,4 of 3 30 pT
Propello Tetrakis Hexahedron (canonical)  dmccooeyPropellor 86 78 of 4,8 of 6 96 72 of 4,24 of 3 180 pdtO
Propello Truncated Cuboctahedron (canonical)  dmccooeyPropellor 192 144 of 4,48 of 3 170 6 of 8,8 of 6,156 of 4 360 ptaC
Propello Truncated Icosahedron (canonical)  dmccooeyPropellor 240 180 of 4,60 of 3 212 20 of 6,12 of 5,180 of 4 450 ptI
Propello Truncated Icosidodecahedron (canonical)  dmccooeyPropellor 480 360 of 4,120 of 3 422 12 of 10,20 of 6,390 of 4 900 pkD
Propello Truncated Octahedron (canonical)  dmccooeyPropellor 96 72 of 4,24 of 3 86 8 of 6,78 of 4 180 ptO
pyD  CW designs pyD
Rainkis-Hexa  OBrien k(h=-0.02)S3k(h=1.0)C
Random zonohedron with 42 faces  Hart 44 8 of 5,20 of 4,16 of 3 42 42 of 4 84
Rectified Truncated Icosahedron  dmccooeyDerived 90 90 of 4 92 20 of 6,12 of 5,60 of 3 180
Regular Hexagonal Toroid with 10 faces (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 20 20 of 3 10 10 of 6 28
Regular Hexagonal Toroid with 11 faces  dmccooeyRegular Hexagonal Toroidalconcave 22 22 of 3 11 11 of 6 31
Regular Hexagonal Toroid with 12 faces (type A) (trapezohedral form)  dmccooeyRegular Hexagonal Toroidalconcave 24 24 of 3 12 12 of 6 34
Regular Hexagonal Toroid with 12 faces (type B)  dmccooeyRegular Hexagonal Toroidalconcave 24 24 of 3 12 12 of 6 34
Regular Hexagonal Toroid with 12 faces (type C) (knot form)  dmccooeyRegular Hexagonal Toroidalconcave 24 24 of 3 12 12 of 6 34
Regular Hexagonal Toroid with 12 faces (type C) (simple form)  dmccooeyRegular Hexagonal Toroidalconcave 24 24 of 3 12 12 of 6 34
Regular Hexagonal Toroid with 12 faces (type D) (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 24 24 of 3 12 12 of 6 34
Regular Hexagonal Toroid with 13 faces (type A)  dmccooeyRegular Hexagonal Toroidalconcave 26 26 of 3 13 13 of 6 37
Regular Hexagonal Toroid with 13 faces (type B) (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 26 26 of 3 13 13 of 6 37
Regular Hexagonal Toroid with 14 faces (type A) (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 28 28 of 3 14 14 of 6 40
Regular Hexagonal Toroid with 14 faces (type B)  dmccooeyRegular Hexagonal Toroidalconcave 28 28 of 3 14 14 of 6 40
Regular Hexagonal Toroid with 15 faces (type A) (knot form 2)  dmccooeyRegular Hexagonal Toroidalconcave 30 30 of 3 15 15 of 6 43
Regular Hexagonal Toroid with 15 faces (type A) (version 1)  dmccooeyRegular Hexagonal Toroidalconcave 30 30 of 3 15 15 of 6 43
Regular Hexagonal Toroid with 15 faces (type D) (version 6)  dmccooeyRegular Hexagonal Toroidalconcave 30 30 of 3 15 15 of 6 43
Regular Hexagonal Toroid with 24 faces  dmccooeyRegular Hexagonal Toroidalconcave 48 48 of 3 24 24 of 6 70
Regular Hexagonal Toroid with 8 faces (D2 symmetry)  dmccooeyRegular Hexagonal Toroidalconcave 16 16 of 3 8 8 of 6 22
Regular Hexagonal Toroid with 8 faces (version 1)  dmccooeyRegular Hexagonal Toroidalconcave 16 16 of 3 8 8 of 6 22
Regular Hexagonal Toroid with 9 faces (type A) (cubic form)  dmccooeyRegular Hexagonal Toroidalconcave 18 18 of 3 9 9 of 6 25
Regular Hexagonal Toroid with 9 faces (type A) (triangular form)  dmccooeyRegular Hexagonal Toroidalconcave 18 18 of 3 9 9 of 6 25
Regular Hexagonal Toroid with 9 faces (type B)  dmccooeyRegular Hexagonal Toroidalconcave 18 18 of 3 9 9 of 6 25
Regular Map {4,6}10 (Schulte & Wills)  dmccooeyHigher Genus Toroidalconcave 20 20 of 6 30 30 of 4 48
Regular Map {6,4}10 (Schulte & Wills)  dmccooeyHigher Genus Toroidalconcave 30 30 of 4 20 20 of 6 48
Regular Tetragonal Toroid with 18 faces (type A) (version 1)  dmccooeyRegular Tetragonal Toroidalconcave 18 18 of 4 18 18 of 4 34
Regular Tetragonal Toroid with 18 faces (type A) (version 2)  dmccooeyRegular Tetragonal Toroidalconcave 18 18 of 4 18 18 of 4 34
Regular Tetragonal Toroid with 18 faces (type B) (antiprismatic form)  dmccooeyRegular Tetragonal Toroidalconcave 18 18 of 4 18 18 of 4 34
Regular Tetragonal Toroid with 18 faces (type B) (cubic form)  dmccooeyRegular Tetragonal Toroidalconcave 18 18 of 4 18 18 of 4 34
Regular Tetragonal Toroid with 9 faces  dmccooeyRegular Tetragonal Toroidalconcave 9 9 of 4 9 9 of 4 16
Regular Triangular Toroid with 16 faces  dmccooeyRegular Triangular Toroidalconcave 8 8 of 6 16 16 of 3 22
Regular Triangular Toroid with 18 faces (type A) (triangular form)  dmccooeyRegular Triangular Toroidalconcave 9 9 of 6 18 18 of 3 25
Regular Triangular Toroid with 18 faces (type B)  dmccooeyRegular Triangular Toroidalconcave 9 9 of 6 18 18 of 3 25
Regular Triangular Toroid with 20 faces  dmccooeyRegular Triangular Toroidalconcave 10 10 of 6 20 20 of 3 28
Regular Triangular Toroid with 22 faces  dmccooeyRegular Triangular Toroidalconcave 11 11 of 6 22 22 of 3 31
Regular Triangular Toroid with 24 faces (type A) (square form)  dmccooeyRegular Triangular Toroidalconcave 12 12 of 6 24 24 of 3 34
Regular Triangular Toroid with 24 faces (type B)  dmccooeyRegular Triangular Toroidalconcave 12 12 of 6 24 24 of 3 34
Regular Triangular Toroid with 24 faces (type C)  dmccooeyRegular Triangular Toroidalconcave 12 12 of 6 24 24 of 3 34
Regular Triangular Toroid with 24 faces (type D)  dmccooeyRegular Triangular Toroidalconcave 12 12 of 6 24 24 of 3 34
Rhombic Dodecahedron  dmccooeyCatalanisohedron 14 6 of 4,8 of 3 12 12 of 4 24 jC
Rhombic Dodecahemioctahedron  Space-fillingconcave 13 4 of 4,8 of 5,1 of 8 20 16 of 3,4 of 4 31
Rhombic Enneacontahedron  Hart 92 12 of 5,60 of 3,20 of 6 90 90 of 4 180 jtI
Rhombic Enneacontahedron  dmccooeyOther 92 20 of 6,60 of 3,12 of 5 90 90 of 4 180
Rhombic Hexecontahedron  Otherdmccooey 62 30 of 4,20 of 3,12 of 5 60 60 of 4 120
Rhombic Icosahedron  dmccooeyOther 22 10 of 4,10 of 3,2 of 5 20 20 of 4 40
Rhombic Triacontahedron  dmccooeyCatalanisohedron 32 12 of 5,20 of 3 30 30 of 4 60 gD
Rhombicosacron  dmccooeyVersi-Quasi-Regular Dualsconcave 50 20 of 6,30 of 4 60 60 of 4 108
Rhombicosahedron  dmccooeyVersi-Quasi-Regularconcave 60 60 of 4 50 20 of 6,30 of 4 108
Rhombicosidodecahedron  dmccooeyArchimedean 60 60 of 4 62 12 of 5,30 of 4,20 of 3 120 aaD
Rhombicuboctahedron  dmccooeyArchimedean 24 24 of 4 26 18 of 4,8 of 3 48 eO, eC, aaC
Rhombidodecadodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 54 24 of 5,30 of 4 112
Schönhardt Polyhedron  dmccooeyconcaveOther 6 6 of 4 8 8 of 3 12
Self-Dual Icosioctahedron #1 (canonical)  dmccooeyGreater Self-Dual 28 12 of 4,12 of 3,4 of 6 28 4 of 6,12 of 4,12 of 3 54
Self-Dual Icosioctahedron #2 (canonical)  dmccooeyGreater Self-Dual 28 12 of 5,16 of 3 28 12 of 5,16 of 3 54
Self-Dual Icosioctahedron #3 (canonical)  dmccooeyGreater Self-Dual 28 12 of 5,16 of 3 28 12 of 5,16 of 3 54
Self-Dual Icosioctahedron #4 (canonical)  dmccooeyGreater Self-Dual 28 24 of 4,4 of 3 28 24 of 4,4 of 3 54
Self-Dual Tetracontahedron #1 (canonical)  dmccooeyGreater Self-Dual 40 12 of 4,24 of 3,4 of 9 40 4 of 9,12 of 4,24 of 3 78
Self-Dual Tetracontahedron #2 (canonical)  dmccooeyGreater Self-Dual 40 12 of 5,24 of 3,4 of 6 40 4 of 6,12 of 5,24 of 3 78
Self-Dual Tetracontahedron #3 (canonical)  dmccooeyGreater Self-Dual 40 12 of 6,28 of 3 40 12 of 6,28 of 3 78
Self-Dual Tetracontahedron #4 (canonical)  dmccooeyGreater Self-Dual 40 12 of 4,16 of 3,12 of 5 40 12 of 5,12 of 4,16 of 3 78
Self-Dual Tetracontahedron #5 (canonical)  dmccooeyGreater Self-Dual 40 12 of 4,12 of 5,16 of 3 40 12 of 5,12 of 4,16 of 3 78
Self-Dual Tetracontahedron #6 (canonical)  dmccooeyGreater Self-Dual 40 12 of 5,16 of 3,12 of 4 40 12 of 5,12 of 4,16 of 3 78
skkC  CW designs skkC
Small Cubicuboctahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 24 24 of 4 20 6 of 8,6 of 4,8 of 3 42
Small Ditrigonal Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12 of 10,20 of 3,12 of 5 60 60 of 4 102
Small Ditrigonal Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 44 12 of 10,12 of 5,20 of 3 102
Small Ditrigonal Icosidodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 20 20 of 6 32 12 of 5,20 of 3 50
Small Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12 of 10,20 of 3,12 of 5 60 60 of 4 102
Small Dodecahemicosahedron  dmccooeyVersi-Regularconcave 30 30 of 4 22 10 of 6,12 of 5 50
Small Dodecahemidodecahedron  dmccooeyVersi-Regularconcave 30 30 of 4 18 6 of 10,12 of 5 46 k(h=-0.94,fn=[3])aD
Small Dodecicosacron  dmccooeyVersi-Quasi-Regular Dualsconcave 32 12 of 10,20 of 6 60 60 of 4 90
Small Dodecicosahedron  dmccooeyVersi-Quasi-Regularconcave 60 60 of 4 32 12 of 10,20 of 6 90
Small Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 44 12 of 10,12 of 5,20 of 3 102
Small Hexacronic Icositetrahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 20 6 of 8,6 of 4,8 of 3 24 24 of 4 42
Small Hexagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 112 100 of 3,12 of 5 60 60 of 6 170
Small Hexagrammic Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 112 100 of 3,12 of 5 60 60 of 6 170
Small Icosacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 52 20 of 6,12 of 5,20 of 3 60 60 of 4 110
Small Icosicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 52 20 of 6,12 of 5,20 of 3 110
Small Icosihemidodecahedron  dmccooeyVersi-Regularconcave 30 30 of 4 26 6 of 10,20 of 3 54 k(5,h=0.5)aD
Small Retrosnub Icosicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 6 112 12 of 5,100 of 3 170
Small Rhombidodecacron  dmccooeyVersi-Quasi-Regular Dualsconcave 42 12 of 10,30 of 4 60 60 of 4 100
Small Rhombidodecahedron  dmccooeyVersi-Quasi-Regularconcave 60 60 of 4 42 12 of 10,30 of 4 100
Small Rhombihexacron  dmccooeyVersi-Quasi-Regular Dualsconcave 18 6 of 8,12 of 4 24 24 of 4 40
Small Rhombihexahedron  dmccooeyVersi-Quasi-Regularconcave 24 24 of 4 18 6 of 8,12 of 4 40
Small Snub Icosicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 6 112 12 of 5,100 of 3 170
Small Stellapentakis Dodecahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 24 12 of 10,12 of 5 60 60 of 3 82
Small Stellated Dodecahedron  Stellated Dodecahedron dmccooeyKepler-Poinsotconcave 12 12 of 5 12 12 of 5 22 k(h=1)D
Small Stellated Truncated Dodecahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60 of 3 24 12 of 10,12 of 5 82
Small Triambic Icosahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 32 20 of 3,12 of 5 20 20 of 6 50
Snub Cube  dmccooeychiralArchimedean 24 24 of 5 38 6 of 4,32 of 3 60 sC
Snub Dodecadodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 5 84 24 of 5,60 of 3 142
Snub Dodecahedron  dmccooeychiralArchimedean 60 60 of 5 92 12 of 5,80 of 3 150 sD
Snub Hexpropello Dodecahedron (canonical)  dmccooeyDerived 420 420 of 5 632 60 of 6,12 of 5,560 of 3 1050 swD
Snub Icosidodecadodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60 of 6 104 24 of 5,80 of 3 162
Snub Truncated Icosahedron (canonical)  dmccooeyDerived 180 180 of 5 272 20 of 6,12 of 5,240 of 3 450 stI
Snub Truncated Octahedron (canonical)  dmccooeyDerived 72 72 of 5 110 8 of 6,6 of 4,96 of 3 180 stO
Sphenoid Hendecahedron  Space-filling 11 4 of 3,7 of 4 11 7 of 4,4 of 3 20
Square Antiprism  dmccooeyAntiprisms 8 8 of 4 10 2 of 4,8 of 3 16 A4
Square Antiprism-Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 16 8 of 5,8 of 3 16 8 of 5,8 of 3 30
Square Dipyramid  Octahedron dmccooeyDipyramids and Trapezohedra 6 6 of 4 8 8 of 3 12 dP4
Square Prism (Cube)  dmccooeyPrisms 8 8 of 3 6 6 of 4 12 P4
Stella Octangula  Stellated Octahedron, Tetrahedron-Tetrahedron Compound dmccooeyconcaveOther 8 8 of 3 8 8 of 3 14 y0.65O
Stellated Truncated Hexahedron  dmccooeySelf-Intersecting Truncated Regularconcave 24 24 of 3 14 6 of 8,8 of 3 36
Stewart's G3  dmccooeyconcaveOther 13 7 of 3,3 of 4,3 of 5 13 3 of 5,3 of 4,7 of 3 24
Szilassi Polyhedron (version 1)  dmccooeyRegular Hexagonal Toroidalconcave 14 14 of 3 7 7 of 6 19
Tetracontahedron with equal edges  dmccooeyOther 28 24 of 5,4 of 3 40 12 of 4,28 of 3 66
Tetradyakis Hexahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 20 12 of 8,8 of 6 48 48 of 3 66
Tetragonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 10 2 of 4,8 of 3 8 8 of 4 16 dA4
Tetragonal Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 24 8 of 4,16 of 3 16 16 of 5 38
Tetragonal Trapezohedron-Antiprism Toroid  dmccooeyNon-Regular Toroidalconcave 16 8 of 5,8 of 3 16 8 of 5,8 of 3 30
Tetrahedron  dmccooeyPlatonicisohedrondeltahedron 4 4 of 3 4 4 of 3 6 T, Y3
Tetrahemihexahedron  dmccooeyVersi-Regularconcave 6 6 of 4 7 3 of 4,4 of 3 11
Tetrakis Cuboctahedron (canonical)  dmccooeyDerived 18 6 of 4,12 of 6 32 32 of 3 48 k4aC
Tetrakis Hexahedron  tetrahexahedron dmccooeyCatalanisohedron 14 6 of 4,8 of 6 24 24 of 3 36 kC
Tetrakis Snub Cube (laevo) (canonical)  dmccooeyDerived 30 6 of 4,24 of 6 56 56 of 3 84
Thomson 10  Thomson 10 8 of 5,2 of 4 16 16 of 3 24
Thomson 11  Thomson 11 8 of 5,1 of 6,2 of 4 18 18 of 3 27
Thomson 12  Thomson 12 12 of 5 20 20 of 3 30
Thomson 13  Thomson 13 10 of 5,2 of 6,1 of 4 22 22 of 3 33
Thomson 14  Thomson 14 12 of 5,2 of 6 24 24 of 3 36
Thomson 15  Thomson 15 12 of 5,3 of 6 26 26 of 3 39
Thomson 16  Thomson 16 12 of 5,4 of 6 28 28 of 3 42
Thomson 17  Thomson 17 5 of 6,12 of 5 30 30 of 3 45
Thomson 18  Thomson 18 2 of 4,8 of 6,8 of 5 32 32 of 3 48
Thomson 19  Thomson 19 12 of 5,7 of 6 34 34 of 3 51
Thomson 20  Thomson 20 8 of 6,12 of 5 36 36 of 3 54
Toroid with regular faces  dmccooeyNon-Regular Toroidalconcave 30 15 of 3,12 of 4,3 of 5 24 9 of 6,9 of 4,6 of 3 52
Triakis Icosahedron  dmccooeyCatalanisohedron 32 12 of 10,20 of 3 60 60 of 3 90 kI
Triakis Octahedron  Small Triakis Octahedron, trisoctahedron dmccooeyCatalanisohedron 14 6 of 8,8 of 3 24 24 of 3 36 kO
Triakis Tetrahedron  Tristetrahedron dmccooeyCatalanisohedron 8 4 of 6,4 of 3 12 12 of 3 18 kT
Triangular Antiprism  Octahedron dmccooeyAntiprisms 6 6 of 4 8 8 of 3 12 A3
Triangular Dipyramid  dmccooeyDipyramids and Trapezohedra 5 2 of 3,3 of 4 6 6 of 3 9 dP3
Triangular Prism  dmccooeyPrismsSpace-filling 6 6 of 3 5 3 of 4,2 of 3 9 P3
Triangular Pyramid  Tetrahedron Pyramids Y3
Triangulated Square Pyramid  CW designs vvk4Y4
Tridyakis Icosahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 44 24 of 10,20 of 6 120 120 of 3 162
Trigonal Trapezohedron  Cube dmccooeyDipyramids and Trapezohedra 8 8 of 3 6 6 of 4 12 dA3
Truncated Cube  dmccooeyArchimedean 24 24 of 3 14 6 of 8,8 of 3 36 tC
Truncated Cuboctahedron  Great Rhombicuboctahedron dmccooeyArchimedean 48 48 of 3 26 6 of 8,8 of 6,12 of 4 72 NtaC
Truncated Disdyakis Dodecahedron  dmccooeyTruncated Catalan 144 144 of 3 74 6 of 8,56 of 6,12 of 4 216 tmC
Truncated Disdyakis Triacontahedron  dmccooeyTruncated Catalan 360 360 of 3 182 12 of 10,140 of 6,30 of 4 540 tMD
Truncated Dodecadodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 120 120 of 3 54 24 of 10,30 of 4 172
Truncated Dodecahedron  dmccooeyArchimedean 60 60 of 3 32 12 of 10,20 of 3 90 tD
Truncated Great Dodecahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60 of 3 24 12 of 10,12 of 5 82
Truncated Great Icosahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60 of 3 32 20 of 6,12 of 5 90
Truncated Icosahedron  Goldberg(1,1), Soccer Ball, C60 Buckyball dmccooeyGoldbergArchimedean 60 60 of 3 32 20 of 6,12 of 5 90 tI
Truncated Icosidodecahedron  Great Rhombicosidodecahedron dmccooeyArchimedean 120 120 of 3 62 12 of 10,20 of 6,30 of 4 180 bD
Truncated Octahedron  dmccooeyArchimedean 24 24 of 3 14 8 of 6,6 of 4 36 tO
Truncated Pentakis Dodecahedron (canonical)  Goldberg(3,0) dmccooeyGoldbergTruncated CatalanGoldberg 180 180 of 3 92 80 of 6,12 of 5 270 tkD
Truncated Tetrahedron  dmccooeyArchimedean 12 12 of 3 8 4 of 6,4 of 3 18 tT
Truncated Tetrakis Hexahedron (canonical)  dmccooeyTruncated Catalan 72 72 of 3 38 32 of 6,6 of 4 108 tkC
Uniform Great Rhombicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60 of 4 62 12 of 5,30 of 4,20 of 3 120
Uniform Great Rhombicuboctahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 24 24 of 4 26 18 of 4,8 of 3 48