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group : dmccooey   Count = 450
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Name Groups #Vertices Vertex orders #Faces Face orders #Edges Conway
10-Truncated Triakis Icosahedron (canonical)  dmccooeyTruncated Catalan 140 140{3} 72 12{10}+60{5} 210 t10kI
132-pentagon Polyhedron  dmccooeyDerived 200 140{3}+60{4} 132 132{5} 330
4-5-Truncated Deltoidal Hexecontahedron  dmccooeyTruncated Catalan 200 200{3} 102 60{7}+12{5}+30{4} 300
4-Truncated Deltoidal Icositetrahedron (canonical)  dmccooeyTruncated Catalan 80 80{3} 42 24{7}+18{4} 120 t4oO
6-Truncated Joined Truncated Tetrahedron (canonical)  dmccooeyDerived 40 40{3} 22 10{6}+12{5} 60 t6jtT
6-Truncated Pentakis Dodecahedron (canonical)  dmccooeyTruncated Catalan 132 120{3}+12{5} 80 20{6}+60{5} 210 t6kD
6-Truncated Tetrakis Hexahedron (canonical)  dmccooeyTruncated Catalan 54 6{4}+48{3} 32 8{6}+24{5} 84 t6kC
6-Truncated Triakis Tetrahedron (canonical)  dmccooeyTruncated Catalan 28 28{3} 16 4{6}+12{5} 42 t6kT
8-Truncated Triakis Octahedron (canonical)  dmccooeyTruncated Catalan 56 56{3} 30 6{8}+24{5} 84 t8kO
Anti-Heptagonal Iris Toroid  dmccooeyRegular Triangular Toroidalconcave 14 14{6} 28 28{3} 40
Anti-Hexagonal Iris Toroid  dmccooeyRegular Triangular Toroidalconcave 12 12{6} 24 24{3} 34
Anti-Octagonal Iris Toroid #1  dmccooeyRegular Triangular Toroidalconcave 16 16{6} 32 32{3} 46
Anti-Octagonal Iris Toroid #2  dmccooeyRegular Triangular Toroidalconcave 16 16{6} 32 32{3} 46
Associahedron (canonical)  dmccooeyOther 14 14{3} 9 6{5}+3{4} 21
Bilinski's Dodecahedron  Otherdmccooey 14 6{4}+8{3} 12 12{4} 24
Biscribed Disdyakis Dodecahedron  dmccooeyBiscribed Non-Chiral 26 6{8}+12{4}+8{6} 48 48{3} 72
Biscribed Disdyakis Triacontahedron  dmccooeyBiscribed Non-Chiral 62 30{4}+20{6}+12{10} 120 120{3} 180
Biscribed Dual Snub Truncated Icosahedron  dmccooeyBiscribed Chiral 272 240{3}+20{6}+12{5} 180 180{5} 450
Biscribed Dual Snub Truncated Octahedron  dmccooeyBiscribed Chiral 110 6{4}+96{3}+8{6} 72 72{5} 180
Biscribed Hexpropello Cube (dextro)  dmccooeyBiscribed Chiral 56 56{3} 30 24{6}+6{4} 84
Biscribed Hexpropello Dodecahedron (dextro)  dmccooeyBiscribed Chiral 140 140{3} 72 60{6}+12{5} 210
Biscribed L-Propello L-Snub Cube  dmccooeyBiscribed Chiral 144 120{4}+24{5} 158 126{4}+32{3} 300
Biscribed L-Propello R-pentagonal Icositetrahedron  dmccooeyBiscribed Chiral 158 126{4}+32{3} 144 24{5}+120{4} 300
Biscribed Orthokis Propello Cube  dmccooeyBiscribed Chiral 38 6{4}+24{5}+8{3} 48 24{4}+24{3} 84
Biscribed Orthokis Propello Dodecahedron  dmccooeyBiscribed Chiral 92 72{5}+20{3} 120 60{4}+60{3} 210
Biscribed Orthotruncated Propello Icosahedron  dmccooeyBiscribed Chiral 120 60{4}+60{3} 92 72{5}+20{3} 210
Biscribed Orthotruncated Propello Octahedron  dmccooeyBiscribed Chiral 48 24{3}+24{4} 38 24{5}+6{4}+8{3} 84
Biscribed pentagonal Hexecontahedron (dextro)  dmccooeyBiscribed Chiral 92 80{3}+12{5} 60 60{5} 150
Biscribed pentagonal Icositetrahedron (dextro)  dmccooeyBiscribed Chiral 38 6{4}+32{3} 24 24{5} 60
Biscribed Pentakis Dodecahedron  dmccooeyBiscribed Non-Chiral 32 20{6}+12{5} 60 60{3} 90
Biscribed Pentakis Snub Dodecahedron (laevo)  dmccooeyBiscribed Chiral 72 60{6}+12{5} 140 140{3} 210
Biscribed Propello Cube  dmccooeyBiscribed Chiral 32 24{4}+8{3} 30 30{4} 60
Biscribed Propello Disdyakis Dodecahedron  dmccooeyBiscribed Chiral 170 6{8}+156{4}+8{6} 192 144{4}+48{3} 360
Biscribed Propello Disdyakis Triacontahedron  dmccooeyBiscribed Chiral 422 390{4}+20{6}+12{10} 480 360{4}+120{3} 900
Biscribed Propello Dodecahedron  dmccooeyBiscribed Chiral 80 60{4}+20{3} 72 12{5}+60{4} 150
Biscribed Propello Icosahedron  dmccooeyBiscribed Chiral 72 60{4}+12{5} 80 60{4}+20{3} 150
Biscribed Propello Octahedron  dmccooeyBiscribed Chiral 30 30{4} 32 24{4}+8{3} 60
Biscribed Propello Pentakis Dodecahedron  dmccooeyBiscribed Chiral 212 180{4}+20{6}+12{5} 240 180{4}+60{3} 450
Biscribed Propello Tetrahedron  dmccooeyBiscribed Chiral 16 12{4}+4{3} 16 12{4}+4{3} 30
Biscribed Propello Tetrakis Hexahedron  dmccooeyBiscribed Chiral 86 78{4}+8{6} 96 72{4}+24{3} 180
Biscribed Propello Truncated Cuboctahedron  dmccooeyBiscribed Chiral 192 144{4}+48{3} 170 6{8}+8{6}+156{4} 360
Biscribed Propello Truncated Icosahedron  dmccooeyBiscribed Chiral 240 180{4}+60{3} 212 20{6}+12{5}+180{4} 450
Biscribed Propello Truncated Icosidodecahedron  dmccooeyBiscribed Chiral 480 360{4}+120{3} 422 12{10}+20{6}+390{4} 900
Biscribed Propello Truncated Octahedron  dmccooeyBiscribed Chiral 96 72{4}+24{3} 86 8{6}+78{4} 180
Biscribed Snub Cube (laevo)  dmccooeyBiscribed Chiral 24 24{5} 38 6{4}+32{3} 60
Biscribed Snub Dodecahedron (laevo)  dmccooeyBiscribed Chiral 60 60{5} 92 12{5}+80{3} 150
Biscribed Snub Truncated Icosahedron  dmccooeyBiscribed Chiral 180 180{5} 272 20{6}+12{5}+240{3} 450
Biscribed Snub Truncated Octahedron  dmccooeyBiscribed Chiral 72 72{5} 110 8{6}+6{4}+96{3} 180
Biscribed Tetrakis Hexahedron  dmccooeyBiscribed Non-Chiral 14 6{4}+8{6} 24 24{3} 36
Biscribed Tetrakis Snub Cube (laevo)  dmccooeyBiscribed Chiral 30 6{4}+24{6} 56 56{3} 84
Biscribed Truncated Cuboctahedron  dmccooeyBiscribed Non-Chiral 48 48{3} 26 6{8}+8{6}+12{4} 72
Biscribed Truncated Icosahedron  dmccooeyBiscribed Non-Chiral 60 60{3} 32 20{6}+12{5} 90
Biscribed Truncated Icosidodecahedron  dmccooeyBiscribed Non-Chiral 120 120{3} 62 12{10}+20{6}+30{4} 180
Biscribed Truncated Octahedron  dmccooeyBiscribed Non-Chiral 24 24{3} 14 8{6}+6{4} 36
Borromean Rings  dmccooeyRegular Tetragonal Toroidalconcave 36 36{4} 36 36{4} 70
Cairo-Tiling Toroid with 16 faces (type A) (8 faces overarching)  dmccooeyNon-Regular Toroidalconcave 24 16{3}+8{4} 16 16{5} 38
Cairo-Tiling Toroid with 16 faces (type B) (square form)  dmccooeyNon-Regular Toroidalconcave 24 16{3}+8{4} 16 16{5} 38
Cairo-Tiling Toroid with 16 faces (type C) (boomerang form)  dmccooeyNon-Regular Toroidalconcave 24 8{4}+16{3} 16 16{5} 38
Cairo-Tiling Toroid with 8 overarching faces (version 1)  dmccooeyNon-Regular Toroidalconcave 12 8{3}+4{4} 8 8{5} 18
Canonical Joined Truncated Icosahedron  dmccooeyOther 92 20{6}+60{3}+12{5} 90 90{4} 180 jtI
Chamfered Cube (all edges equal)  dmccooeyChamfered 32 32{3} 18 12{6}+6{4} 48 cC
Chamfered Dodecahedron (all edges equal)  dmccooeyChamfered 80 80{3} 42 30{6}+12{5} 120 cD
Chamfered Icosahedron (all edges equal)  dmccooeyChamfered 72 12{5}+60{3} 50 30{6}+20{3} 120 cI
Chamfered Octahedron (all edges equal)  dmccooeyChamfered 30 6{4}+24{3} 20 12{6}+8{3} 48 cO
Chamfered Tetrahedron (all edges equal)  dmccooeyChamfered 16 16{3} 10 6{6}+4{3} 24 cT
Chamfered Truncated Icosahedron (canonical)  Goldberg(2,2) dmccooeyChamferedGoldberg 240 240{3} 122 110{6}+12{5} 360 ctI
Concave Dodecahedron  dmccooeyconcaveOther 20 20{3} 12 12{5} 30
Császár Polyhedron (version 4)  dmccooeyRegular Triangular Toroidalconcave 7 7{6} 14 14{3} 19
Cube  Hexahedron dmccooeyPlatonicisohedronSpace-fillingisotoxal 8 8{3} 6 6{4} 12 C, jY3
Cube-Octahedron Compound  dmccooeyconcaveOther 14 8{3}+6{4} 14 6{4}+8{3} 26 y0.57C
Cube-Octahedron Toroid  dmccooeyNon-Regular Toroidalconcave 12 6{3}+6{5} 12 6{5}+6{3} 22
Cubitruncated Cuboctahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 48 48{3} 20 12{8}+8{6} 66
Cuboctahedron  dmccooeyArchimedeanisotoxal 12 12{4} 14 6{4}+8{3} 24 aC
Cubohemioctahedron  dmccooeyVersi-Regularconcave 12 12{4} 10 4{6}+6{4} 20 k(h=-0.65,fn=[3])aC
Deltoidal Hexecontahedron  dmccooeyCatalanisohedron 62 30{4}+20{3}+12{5} 60 60{4} 120 oD
Deltoidal Icositetrahedron  dmccooeyCatalanisohedron 26 18{4}+8{3} 24 24{4} 48 oO
Disdyakis Dodecahedron  Hexakis Octahedron dmccooeyCatalanisohedron 26 6{8}+12{4}+8{6} 48 48{3} 72 mC, mO
Disdyakis Triacontahedron  Hexakis Icosahedron dmccooeyCatalanisohedron 62 30{4}+20{6}+12{10} 120 120{3} 180 mD
Ditrigonal Dodecadodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 20 20{6} 24 24{5} 42
Dodecadodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 30 30{4} 24 24{5} 52
Dodecahedron  Goldberg(0,1) dmccooeyGoldbergPlatonicisohedronisotoxal 20 20{3} 12 12{5} 30 D, gY3
Dodecahedron-Icosahedron Compound  dmccooeyconcaveOther 32 20{3}+12{5} 32 12{5}+20{3} 62 y0.3D
Dual Geodesic Icosahedron Pattern 1 [1,1]  Truncated Icosahedron, Goldberg(1,1) dmccooeyDual Geodesic IcosahedraGoldberg 60 60{3} 32 20{6}+12{5} 90 tI, dkD
Dual Geodesic Icosahedron Pattern 10 [5,0]  Goldberg(5,0) dmccooeyDual Geodesic IcosahedraGoldberg 500 500{3} 252 12{5}+240{6} 750
Dual Geodesic Icosahedron Pattern 11 [3,3]  Goldberg(3,3) dmccooeyDual Geodesic IcosahedraGoldberg 540 540{3} 272 12{5}+260{6} 810 tktI
Dual Geodesic Icosahedron Pattern 12 [4,2]  Goldberg(4,2) dmccooeyDual Geodesic IcosahedraGoldberg 560 560{3} 282 12{5}+270{6} 840 wcD
Dual Geodesic Icosahedron Pattern 13 [5,1]  Goldberg(5,1) dmccooeyDual Geodesic IcosahedraGoldberg 620 620{3} 312 12{5}+300{6} 930
Dual Geodesic Icosahedron Pattern 14 [6,0]  Goldberg(6,0) dmccooeyDual Geodesic IcosahedraGoldberg 720 720{3} 362 12{5}+350{6} 1080 ctkD, cdktI, tkt5daD
Dual Geodesic Icosahedron Pattern 15 [4,3]  Goldberg(4,3) dmccooeyDual Geodesic IcosahedraGoldberg 740 740{3} 372 12{5}+360{6} 1110
Dual Geodesic Icosahedron Pattern 16 [5,2]  Goldberg(5,2) dmccooeyDual Geodesic IcosahedraGoldberg 780 780{3} 392 12{5}+380{6} 1170
Dual Geodesic Icosahedron Pattern 17 [6,1]  Goldberg(6,1) dmccooeyDual Geodesic IcosahedraGoldberg 860 860{3} 432 12{5}+420{6} 1290
Dual Geodesic Icosahedron Pattern 18 [4,4]  Goldberg(4,4) dmccooeyDual Geodesic IcosahedraGoldberg 960 960{3} 482 12{5}+470{6} 1440 dkt5dadkt5daD, cctI
Dual Geodesic Icosahedron Pattern 19 [7,0]  Goldberg(7,0) dmccooeyDual Geodesic IcosahedraGoldberg 980 980{3} 492 12{5}+480{6} 1470
Dual Geodesic Icosahedron Pattern 2 [2,0]  Chamfered Dodecahedron, Goldberg(2,0) dmccooeyDual Geodesic IcosahedraGoldberg 80 80{3} 42 30{6}+12{5} 120 cD
Dual Geodesic Icosahedron Pattern 20 [5,3]  Goldberg(5,3) dmccooeyDual Geodesic IcosahedraGoldberg 980 980{3} 492 12{5}+480{6} 1470 wwD
Dual Geodesic Icosahedron Pattern 21 [6,2]  Goldberg(6,2) dmccooeyDual Geodesic IcosahedraGoldberg 1040 1040{3} 522 12{5}+510{6} 1560
Dual Geodesic Icosahedron Pattern 22 [7,1]  Goldberg(7,1) dmccooeyDual Geodesic IcosahedraGoldberg 1140 1140{3} 572 12{5}+560{6} 1710
Dual Geodesic Icosahedron Pattern 23 [5,4]  Goldberg(5,4) dmccooeyDual Geodesic IcosahedraGoldberg 1220 1220{3} 612 12{5}+600{6} 1830
Dual Geodesic Icosahedron Pattern 24 [6,3]  Goldberg(6,3) dmccooeyDual Geodesic IcosahedraGoldberg 1260 1260{3} 632 12{5}+620{6} 1890
Dual Geodesic Icosahedron Pattern 25 [8,0]  Goldberg(8,0) dmccooeyDual Geodesic IcosahedraGoldberg 1280 1280{3} 642 12{5}+630{6} 1920 cccD
Dual Geodesic Icosahedron Pattern 3 [2,1]  Hexpropello Dodecahedron, Goldberg(2,1) dmccooeyDual Geodesic IcosahedraGoldberg 140 140{3} 72 60{6}+12{5} 210 wD, dk5sD, t5gD
Dual Geodesic Icosahedron Pattern 4 [3,0]  Truncated Pentakis Dodecahedron, Goldberg(3,0) dmccooeyDual Geodesic IcosahedraGoldberg 180 180{3} 92 80{6}+12{5} 270 tkD, dktI, tdtI
Dual Geodesic Icosahedron Pattern 5 [2,2]  Truncated Pentakis Icosidodecahedron, Goldberg(2,2) dmccooeyDual Geodesic IcosahedraGoldberg 240 240{3} 122 110{6}+12{5} 360 ctI, dkt5daD
Dual Geodesic Icosahedron Pattern 6 [3,1]  Goldberg(3,1) dmccooeyDual Geodesic IcosahedraGoldberg 260 260{3} 132 12{5}+120{6} 390
Dual Geodesic Icosahedron Pattern 7 [4,0]  Goldberg(4,0) dmccooeyDual Geodesic IcosahedraGoldberg 320 320{3} 162 12{5}+150{6} 480 ccD
Dual Geodesic Icosahedron Pattern 8 [3,2]  Goldberg(3,2) dmccooeyDual Geodesic IcosahedraGoldberg 380 380{3} 192 12{5}+180{6} 570
Dual Geodesic Icosahedron Pattern 9 [4,1]  Goldberg(4,1) dmccooeyDual Geodesic IcosahedraGoldberg 420 420{3} 212 12{5}+200{6} 630 tk5sD
Dual Snub Hexpropello Dodecahedron (canonical)  dmccooeyDerived 632 560{3}+60{6}+12{5} 420 420{5} 1050 dswD
Dual Snub Truncated Icosahedron (canonical)  dmccooeyDerived 272 240{3}+20{6}+12{5} 180 180{5} 450 dstI
Dual Snub Truncated Octahedron (canonical)  dmccooeyDerived 110 6{4}+96{3}+8{6} 72 72{5} 180 dstO
Dürer's Solid  dmccooeyOther 12 12{3} 8 6{5}+2{3} 18
Elongated Square Gyrobicupola  dmccooeyOther 24 24{4} 26 18{4}+8{3} 48
Escher's Solid  dmccooeyconcaveOther 26 6{8}+12{4}+8{6} 48 48{3} 72 k(h=0.76)KjC
Expanded Joined Hexpropello Dodecahedron (canonical)  dmccooeyDerived 840 840{4} 842 60{6}+12{5}+630{4}+140{3} 1680 ejwD
Expanded Joined Truncated Pentakis Dodecahedron (canonical)  dmccooeyDerived 1080 1080{4} 1082 80{6}+12{5}+810{4}+180{3} 2160 ejtkD
Expanded Propello Truncated Icosahedron (canonical)  dmccooeyDerived 900 900{4} 902 20{6}+12{5}+810{4}+60{3} 1800 eptI
Geodesic Cube Pattern 10 [3,3]  dmccooeyGeodesic Cubes 110 102{4}+8{3} 108 108{4} 216
Geodesic Cube Pattern 11 [4,2]  dmccooeyGeodesic Cubes 122 114{4}+8{3} 120 120{4} 240 oKpC
Geodesic Cube Pattern 12 [5,0]  dmccooeyGeodesic Cubes 152 144{4}+8{3} 150 150{4} 300 pKpC
Geodesic Cube Pattern 13 [4,3]  dmccooeyGeodesic Cubes 152 144{4}+8{3} 150 150{4} 300
Geodesic Cube Pattern 14 [5,1]  dmccooeyGeodesic Cubes 158 150{4}+8{3} 156 156{4} 312
Geodesic Cube Pattern 15 [5,2]  dmccooeyGeodesic Cubes 176 168{4}+8{3} 174 174{4} 348
Geodesic Cube Pattern 2 [2,0]  Deltoidal Icositetrahedron dmccooeyGeodesic Cubes 26 18{4}+8{3} 24 24{4} 48 oC
Geodesic Cube Pattern 3 [2,1]  Propello Cube dmccooeyGeodesic Cubes 32 24{4}+8{3} 30 30{4} 60 pC
Geodesic Cube Pattern 4 [2,2]  dmccooeyGeodesic Cubes 50 42{4}+8{3} 48 48{4} 96 ojC
Geodesic Cube Pattern 5 [3,0]  dmccooeyGeodesic Cubes 56 48{4}+8{3} 54 54{4} 108
Geodesic Cube Pattern 6 [3,1]  dmccooeyGeodesic Cubes 62 54{4}+8{3} 60 60{4} 120 jKpC
Geodesic Cube Pattern 7 [3,2]  dmccooeyGeodesic Cubes 80 72{4}+8{3} 78 78{4} 156
Geodesic Cube Pattern 8 [4,0]  dmccooeyGeodesic Cubes 98 90{4}+8{3} 96 96{4} 192 ooC
Geodesic Cube Pattern 9 [4,1]  dmccooeyGeodesic Cubes 104 96{4}+8{3} 102 102{4} 204
Geodesic Icosahedron Pattern 1 [1,1]  Pentakis Dodecahedron dmccooeyGeodesic Icosahedra 32 20{6}+12{5} 60 60{3} 90 kI, kD
Geodesic Icosahedron Pattern 10 [5,0]  dmccooeyGeodesic Icosahedra 252 240{6}+12{5} 500 500{3} 750
Geodesic Icosahedron Pattern 11 [3,3]  dmccooeyGeodesic Icosahedra 272 260{6}+12{5} 540 540{3} 810
Geodesic Icosahedron Pattern 12 [4,2]  dmccooeyGeodesic Icosahedra 282 270{6}+12{5} 560 560{3} 840
Geodesic Icosahedron Pattern 13 [5,1]  dmccooeyGeodesic Icosahedra 312 300{6}+12{5} 620 620{3} 930
Geodesic Icosahedron Pattern 14 [6,0]  dmccooeyGeodesic Icosahedra 362 350{6}+12{5} 720 720{3} 1080
Geodesic Icosahedron Pattern 15 [4,3]  dmccooeyGeodesic Icosahedra 372 360{6}+12{5} 740 740{3} 1110
Geodesic Icosahedron Pattern 16 [5,2]  dmccooeyGeodesic Icosahedra 392 380{6}+12{5} 780 780{3} 1170
Geodesic Icosahedron Pattern 17 [6,1]  dmccooeyGeodesic Icosahedra 432 420{6}+12{5} 860 860{3} 1290
Geodesic Icosahedron Pattern 18 [4,4]  dmccooeyGeodesic Icosahedra 482 470{6}+12{5} 960 960{3} 1440
Geodesic Icosahedron Pattern 19 [7,0]  dmccooeyGeodesic Icosahedra 492 480{6}+12{5} 980 980{3} 1470
Geodesic Icosahedron Pattern 2 [2,0]  Pentakis Icosidodecahedron dmccooeyGeodesic Icosahedra 42 30{6}+12{5} 80 80{3} 120 vI, k5aD
Geodesic Icosahedron Pattern 20 [5,3]  dmccooeyGeodesic Icosahedra 492 480{6}+12{5} 980 980{3} 1470
Geodesic Icosahedron Pattern 21 [6,2]  dmccooeyGeodesic Icosahedra 522 510{6}+12{5} 1040 1040{3} 1560
Geodesic Icosahedron Pattern 22 [7,1]  dmccooeyGeodesic Icosahedra 572 560{6}+12{5} 1140 1140{3} 1710
Geodesic Icosahedron Pattern 23 [5,4]  dmccooeyGeodesic Icosahedra 612 600{6}+12{5} 1220 1220{3} 1830
Geodesic Icosahedron Pattern 24 [6,3]  dmccooeyGeodesic Icosahedra 632 620{6}+12{5} 1260 1260{3} 1890
Geodesic Icosahedron Pattern 25 [8,0]  dmccooeyGeodesic Icosahedra 642 630{6}+12{5} 1280 1280{3} 1920
Geodesic Icosahedron Pattern 3 [2,1]  Pentakis Snub Dodecahedron dmccooeyGeodesic Icosahedra 72 60{6}+12{5} 140 140{3} 210 k5sD
Geodesic Icosahedron Pattern 4 [3,0]  Hexakis-Pentakis Truncated Icosahedron dmccooeyGeodesic Icosahedra 92 80{6}+12{5} 180 180{3} 270
Geodesic Icosahedron Pattern 5 [2,2]  Hexakis-Pentakis Chamfered Dodecahedron dmccooeyGeodesic Icosahedra 122 110{6}+12{5} 240 240{3} 360
Geodesic Icosahedron Pattern 6 [3,1]  dmccooeyGeodesic Icosahedra 132 120{6}+12{5} 260 260{3} 390
Geodesic Icosahedron Pattern 7 [4,0]  dmccooeyGeodesic Icosahedra 162 150{6}+12{5} 320 320{3} 480
Geodesic Icosahedron Pattern 8 [3,2]  dmccooeyGeodesic Icosahedra 192 180{6}+12{5} 380 380{3} 570
Geodesic Icosahedron Pattern 9 [4,1]  dmccooeyGeodesic Icosahedra 212 200{6}+12{5} 420 420{3} 630
Great Cubicuboctahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 24 24{4} 20 6{8}+6{4}+8{3} 42
Great Deltoidal Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 62 30{4}+20{3}+12{5} 60 60{4} 120
Great Deltoidal Icositetrahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 26 18{4}+8{3} 24 24{4} 48
Great Dirhombicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{8} 124 24{5}+60{4}+40{3} 182
Great Disdyakis Dodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 26 6{8}+12{4}+8{6} 48 48{3} 72
Great Disdyakis Triacontahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 62 30{4}+20{6}+12{10} 120 120{3} 180
Great Ditrigonal Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12{10}+20{3}+12{5} 60 60{4} 102
Great Ditrigonal Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 44 12{10}+12{5}+20{3} 102
Great Ditrigonal Icosidodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 20 20{6} 32 12{5}+20{3} 50
Great Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12{10}+20{3}+12{5} 60 60{4} 102
Great Dodecahedron  dmccooeyKepler-Poinsotconcave 12 12{5} 12 12{5} 22 k(h=-0.2)I
Great Dodecahemicosahedron  dmccooeyVersi-Regularconcave 30 30{4} 22 10{6}+12{5} 50
Great Dodecahemidodecahedron  dmccooeyVersi-Regularconcave 30 30{4} 18 6{10}+12{5} 46
Great Dodecicosacron  dmccooeyVersi-Quasi-Regular Dualsconcave 32 12{10}+20{6} 60 60{4} 90
Great Dodecicosahedron  dmccooeyVersi-Quasi-Regularconcave 60 60{4} 32 12{10}+20{6} 90
Great Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 44 12{10}+12{5}+20{3} 102
Great Hexacronic Icositetrahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 20 6{8}+6{4}+8{3} 24 24{4} 42
Great Hexagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 104 80{3}+24{5} 60 60{6} 162
Great Icosacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 52 20{6}+12{5}+20{3} 60 60{4} 110
Great Icosahedron  dmccooeyKepler-Poinsotconcave 12 12{5} 20 20{3} 30 k(h=-0.2)k(h=1)D
Great Icosicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 52 20{6}+12{5}+20{3} 110
Great Icosidodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 30 30{4} 32 12{5}+20{3} 60
Great Icosihemidodecahedron  dmccooeyVersi-Regularconcave 30 30{4} 26 6{10}+20{3} 54
Great Inverted pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 92 80{3}+12{5} 60 60{5} 150
Great Inverted Snub Icosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{5} 92 12{5}+80{3} 150
Great pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 92 80{3}+12{5} 60 60{5} 150
Great pentagrammic Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 92 80{3}+12{5} 60 60{5} 150
Great Pentakis Dodecahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 24 12{10}+12{5} 60 60{3} 82
Great Retrosnub Icosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{5} 92 12{5}+80{3} 150
Great Rhombic Triacontahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 32 12{5}+20{3} 30 30{4} 60
Great Rhombidodecacron  dmccooeyVersi-Quasi-Regular Dualsconcave 42 12{10}+30{4} 60 60{4} 100
Great Rhombidodecahedron  dmccooeyVersi-Quasi-Regularconcave 60 60{4} 42 12{10}+30{4} 100
Great Rhombihexacron  dmccooeyVersi-Quasi-Regular Dualsconcave 18 6{8}+12{4} 24 24{4} 40
Great Rhombihexahedron  dmccooeyVersi-Quasi-Regularconcave 24 24{4} 18 6{8}+12{4} 40
Great Snub Dodecicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{6} 104 24{5}+80{3} 162
Great Snub Icosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{5} 92 12{5}+80{3} 150
Great Stellapentakis Dodecahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 32 20{6}+12{5} 60 60{3} 90
Great Stellated Dodecahedron  Stellated Great Dodecahedron dmccooeyKepler-Poinsotconcave 20 20{3} 12 12{5} 30 k(h=1.6)I
Great Stellated Truncated Dodecahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60{3} 32 12{10}+20{3} 90
Great Triakis Icosahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 32 12{10}+20{3} 60 60{3} 90
Great Triakis Octahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 14 6{8}+8{3} 24 24{3} 36
Great Triambic Icosahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 32 20{3}+12{5} 20 20{6} 50
Great Truncated Cuboctahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 48 48{3} 26 6{8}+8{6}+12{4} 72
Great Truncated Icosidodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 120 120{3} 62 12{10}+20{6}+30{4} 180
Gyrate Deltoidal Icositetrahedron  dmccooeyOther 26 18{4}+8{3} 24 24{4} 48
Heptagonal Antiprism  dmccooeyAntiprisms 14 14{4} 16 2{7}+14{3} 28 A7
Heptagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 9 2{7}+7{4} 14 14{3} 21 dP7
Heptagonal Dodecahedron (type A) (C3-symmetric form 3)  dmccooeyHigher Genus Toroidalconcave 28 28{3} 12 12{7} 38
Heptagonal Dodecahedron (type A) (S4-symmetric form 1)  dmccooeyHigher Genus Toroidalconcave 28 28{3} 12 12{7} 38
Heptagonal Dodecahedron (type B) (form 1)  dmccooeyHigher Genus Toroidalconcave 28 28{3} 12 12{7} 38
Heptagonal Dodecahedron (type C) (form 1)  dmccooeyHigher Genus Toroidalconcave 28 28{3} 12 12{7} 38
Heptagonal Dodecahedron (type D) (form 3)  dmccooeyHigher Genus Toroidalconcave 28 28{3} 12 12{7} 38
Heptagonal Dodecahedron (type E) (form 1)  dmccooeyHigher Genus Toroidalconcave 28 28{3} 12 12{7} 38
Heptagonal Iris Toroid  dmccooeyNon-Regular Toroidalconcave 14 14{5} 21 7{4}+14{3} 33
Heptagonal Prism  dmccooeyPrisms 14 14{3} 9 2{7}+7{4} 21 P7
Heptagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 16 2{7}+14{3} 14 14{4} 28 dA7
Heptagrammic 7/2 Antiprism  dmccooeyStar Prisms and Antiprismsconcave 14 14{4} 16 2{7}+14{3} 28
Heptagrammic 7/2 Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 9 2{7}+7{4} 14 14{3} 21
Heptagrammic 7/2 Prism  dmccooeyStar Prisms and Antiprismsconcave 14 14{3} 9 2{7}+7{4} 21
Heptagrammic 7/2 Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 16 2{7}+14{3} 14 14{4} 28
Heptagrammic 7/3 Antiprism  dmccooeyStar Prisms and Antiprismsconcave 14 14{4} 16 2{7}+14{3} 28
Heptagrammic 7/3 Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 9 2{7}+7{4} 14 14{3} 21
Heptagrammic 7/3 Prism  dmccooeyStar Prisms and Antiprismsconcave 14 14{3} 9 2{7}+7{4} 21
Heptagrammic 7/3 Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 16 2{7}+14{3} 14 14{4} 28
Heptagrammic Concave Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 16 2{7}+14{3} 14 14{4} 28
Heptagrammic Crossed Antiprism  dmccooeyStar Prisms and Antiprismsconcave 14 14{4} 16 2{7}+14{3} 28
Hexagonal Antiprism  dmccooeyAntiprisms 12 12{4} 14 2{6}+12{3} 24 A6
Hexagonal Antiprism-Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 24 12{5}+12{3} 24 12{5}+12{3} 46
Hexagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 8 2{6}+6{4} 12 12{3} 18 dP6
Hexagonal Prism  dmccooeyPrismsSpace-filling 12 12{3} 8 2{6}+6{4} 18 P6
Hexagonal Toroid with 8 overarching faces  dmccooeyRegular Hexagonal Toroidalconcave 16 16{3} 8 8{6} 22
Hexagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 14 2{6}+12{3} 12 12{4} 24 dA6
Hexagonal Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 36 12{4}+24{3} 24 24{5} 58
Hexagonal Trapezohedron-Antiprism Toroid  dmccooeyNon-Regular Toroidalconcave 24 12{5}+12{3} 24 12{5}+12{3} 46
Hexpropello Cube (dextro) (canonical)  dmccooeyDerived 56 56{3} 30 24{6}+6{4} 84 wC
Hexpropello Dodecahedron (dextro) (canonical)  dmccooeyDerived 140 140{3} 72 60{6}+12{5} 210 wD
Hugel's Polyhedron  concavedmccooeyOther 20 20{6} 20 20{6} 38 i(r=0.2,h=-0.5)D
Icosahedron  dmccooeyPlatonicisohedrondeltahedronGeodesic Icosahedraisotoxal 12 12{5} 20 20{3} 30 I, sY3, k5aY5
Icosidodecadodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 44 20{6}+24{5} 102
Icosidodecahedron  dmccooeyArchimedeanisotoxal 30 30{4} 32 12{5}+20{3} 60 aD
Icositruncated Dodecadodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 120 120{3} 44 24{10}+20{6} 162
Inverted Snub Dodecadodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{5} 84 24{5}+60{3} 142
Isohedral Toroid with 24 faces  dmccooeyNon-Regular Toroidalconcave 12 6{7}+6{5} 24 24{3} 34
Jessen's Orthogonal Icosahedron  dmccooeyconcaveOther 12 12{5} 20 20{3} 30
Joined Cuboctahedron  dmccooeyArchimedean-Catalan Hulls 26 18{4}+8{3} 24 24{4} 48 jaC
Joined Icosidodecahedron  dmccooeyArchimedean-Catalan Hulls 62 30{4}+20{3}+12{5} 60 60{4} 120 jI
Joined Rhombicosidodecahedron  dmccooeyArchimedean-Catalan Hulls 122 90{4}+20{3}+12{5} 120 120{4} 240 jeD
Joined Rhombicuboctahedron  dmccooeyArchimedean-Catalan Hulls 50 42{4}+8{3} 48 48{4} 96 jeO
Joined Snub Cube (dextro)  dmccooeyArchimedean-Catalan Hulls 62 6{4}+24{5}+32{3} 60 60{4} 120 rjsC
Joined Snub Cube (laevo)  dmccooeyArchimedean-Catalan Hulls 62 6{4}+24{5}+32{3} 60 60{4} 120 jsC
Joined Snub Dodecahedron (dextro)  dmccooeyArchimedean-Catalan Hulls 152 72{5}+80{3} 150 150{4} 300 rjsD
Joined Snub Dodecahedron (laevo)  dmccooeyArchimedean-Catalan Hulls 152 72{5}+80{3} 150 150{4} 300 jsD
Joined Truncated Cube  dmccooeyArchimedean-Catalan Hulls 38 6{8}+32{3} 36 36{4} 72 jtC
Joined Truncated Cuboctahedron  dmccooeyArchimedean-Catalan Hulls 74 6{8}+48{3}+12{4}+8{6} 72 72{4} 144 jaD
Joined Truncated Dodecahedron  dmccooeyArchimedean-Catalan Hulls 92 12{10}+80{3} 90 90{4} 180 jtD
Joined Truncated Icosahedron  dmccooeyArchimedean-Catalan Hulls 92 20{6}+60{3}+12{5} 90 90{4} 180 jtI
Joined Truncated Icosidodecahedron  dmccooeyArchimedean-Catalan Hulls 182 30{4}+120{3}+20{6}+12{10} 180 180{4} 360 jteD
Joined Truncated Octahedron  dmccooeyArchimedean-Catalan HullsSpace-filling 38 6{4}+24{3}+8{6} 36 36{4} 72 jtO
Joined Truncated Tetrahedron  dmccooeyArchimedean-Catalan Hulls 20 4{6}+16{3} 18 18{4} 36 jtT
Klein Map Dual {3,7}8 (Schulte & Wills)  dmccooeyHigher Genus Toroidalconcave 24 24{7} 56 56{3} 78
Klein Map {7,3}8 (basic shape)  dmccooeyHigher Genus Toroidalconcave 56 56{3} 24 24{7} 78
Knotted Dodecahedron  dmccooeyNon-Regular Toroidalconcave 18 12{3}+6{4} 12 6{4}+6{6} 28
L-Propello L-Snub Cube (canonical)  dmccooeyPropellor 144 120{4}+24{5} 158 126{4}+32{3} 300 pdtO
L-Propello R-pentagonal Icositetrahedron (canonical)  dmccooeyPropellor 158 126{4}+32{3} 144 24{5}+120{4} 300 pgC
Medial Deltoidal Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 54 30{4}+24{5} 60 60{4} 112
Medial Disdyakis Triacontahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 54 24{10}+30{4} 120 120{3} 172
Medial Hexagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 104 24{5}+80{3} 60 60{6} 162
Medial Icosacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 20{6}+24{5} 60 60{4} 102
Medial Inverted pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 84 24{5}+60{3} 60 60{5} 142
Medial pentagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 84 24{5}+60{3} 60 60{5} 142
Medial Rhombic Triacontahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 24 24{5} 30 30{4} 52
Medial Triambic Icosahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 24 24{5} 20 20{6} 42
Octagonal Antiprism  dmccooeyAntiprisms 16 16{4} 18 2{8}+16{3} 32 A8
Octagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 10 2{8}+8{4} 16 16{3} 24 dP8
Octagonal Iris Toroid  dmccooeyNon-Regular Toroidalconcave 16 16{5} 24 8{4}+16{3} 38
Octagonal Prism  dmccooeyPrisms 16 16{3} 10 2{8}+8{4} 24 P8
Octagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 18 2{8}+16{3} 16 16{4} 32 dA8
Octagrammic Antiprism  dmccooeyStar Prisms and Antiprismsconcave 16 16{4} 18 2{8}+16{3} 32
Octagrammic Concave Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 18 2{8}+16{3} 16 16{4} 32
Octagrammic Crossed Antiprism  dmccooeyStar Prisms and Antiprismsconcave 16 16{4} 18 2{8}+16{3} 32
Octagrammic Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 10 2{8}+8{4} 16 16{3} 24
Octagrammic Prism  dmccooeyStar Prisms and Antiprismsconcave 16 16{3} 10 2{8}+8{4} 24
Octagrammic Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 18 2{8}+16{3} 16 16{4} 32
Octahedron  Square Dipyramid dmccooeyPlatonicisohedrondeltahedronisotoxal 6 6{4} 8 8{3} 12 O, aY3
Octahemioctahedron  dmccooeyVersi-Regularconcave 12 12{4} 12 4{6}+8{3} 22 k(h=-0.7,fn=[4])aC
Orthokis Propello Cube (canonical)  dmccooeyDerived 38 6{4}+24{5}+8{3} 48 24{4}+24{3} 84 k(regular=true)pC
Orthokis Propello Dodecahedron (canonical)  dmccooeyDerived 92 72{5}+20{3} 120 60{4}+60{3} 210 k(regular=true)pD
Orthotruncated Propello Icosahedron (canonical)  dmccooeyDerived 120 60{4}+60{3} 92 72{5}+20{3} 210
Orthotruncated Propello Octahedron (canonical)  dmccooeyDerived 48 24{3}+24{4} 38 24{5}+6{4}+8{3} 84
pentagonal Antiprism  dmccooeyAntiprisms 10 12 10{3}+2{5} 20 A5
pentagonal Antiprism-Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 20 10{5}+10{3} 20 10{5}+10{3} 38
pentagonal Dipyramid  dmccooeyDipyramids and Trapezohedra 7 2{5}+5{4} 10 10{3} 15 dP5
pentagonal Hexecontahedron  dmccooeyCatalanchiralisohedron 92 80{3}+12{5} 60 60{5} 150 gD
pentagonal Icositetrahedron  gyroid dmccooeychiralCatalanisohedron 38 6{4}+32{3} 24 24{5} 60 gC
pentagonal Prism  dmccooeyPrisms 10 10{3} 7 2{5}+5{4} 15 P5
Pentagonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 12 10{3}+2{5} 10 10{4} 20 dA5
pentagonal Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 30 20{3}+10{4} 20 20{5} 48
pentagonal Trapezohedron-Antiprism Toroid  dmccooeyNon-Regular Toroidalconcave 20 20 10{3}+10{5} 38
Pentagrammic Antiprism  dmccooeyStar Prisms and Antiprismsconcave 10 10{4} 12 2{5}+10{3} 20
pentagrammic Concave Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 12 10{3}+2{5} 10 10{4} 20
Pentagrammic Crossed Antiprism  dmccooeyStar Prisms and Antiprismsconcave 10 10{4} 12 2{5}+10{3} 20
Pentagrammic Dipyramid  dmccooeyStar Dipyramids and Trapezohedraconcave 7 2{5}+5{4} 10 10{3} 15
Pentagrammic Prism  dmccooeyStar Prisms and Antiprismsconcave 10 10{3} 7 2{5}+5{4} 15
pentagrammic Trapezohedron  dmccooeyStar Dipyramids and Trapezohedraconcave 12 10{3}+2{5} 10 10{4} 20
Pentakis Dodecahedron  dmccooeyCatalanisohedronGeodesic Icosahedra 32 20{6}+12{5} 60 60{3} 90 kD
Pentakis Icosidodecahedron (canonical)  dmccooeyDerivedGeodesic Icosahedra 42 30{6}+12{5} 80 80{3} 120
Pentakis Snub Dodecahedron (laevo) (canonical)  dmccooeyDerived 72 60{6}+12{5} 140 140{3} 210
Propello Cube (canonical)  dmccooeyPropellor 32 24{4}+8{3} 30 30{4} 60 pC
Propello Disdyakis Dodecahedron (canonical)  dmccooeyPropellor 170 6{8}+156{4}+8{6} 192 144{4}+48{3} 360 pmC
Propello Disdyakis Triacontahedron (canonical)  dmccooeyPropellor 422 390{4}+20{6}+12{10} 480 360{4}+120{3} 900 pmD
Propello Dodecahedron (canonical)  dmccooeyPropellor 80 60{4}+20{3} 72 12{5}+60{4} 150 pD
Propello Icosahedron (canonical)  dmccooeyPropellor 72 60{4}+12{5} 80 60{4}+20{3} 150 pI
Propello Octahedron (canonical)  dmccooeyPropellor 30 30{4} 32 24{4}+8{3} 60 pO
Propello Pentakis Dodecahedron (canonical)  dmccooeyPropellor 212 180{4}+20{6}+12{5} 240 180{4}+60{3} 450 pkD
Propello Tetrahedron (canonical)  dmccooeyPropellor 16 12{4}+4{3} 16 12{4}+4{3} 30 pT
Propello Tetrakis Hexahedron (canonical)  dmccooeyPropellor 86 78{4}+8{6} 96 72{4}+24{3} 180 pdtO
Propello Truncated Cuboctahedron (canonical)  dmccooeyPropellor 192 144{4}+48{3} 170 6{8}+8{6}+156{4} 360 ptaC
Propello Truncated Icosahedron (canonical)  dmccooeyPropellor 240 180{4}+60{3} 212 20{6}+12{5}+180{4} 450 ptI
Propello Truncated Icosidodecahedron (canonical)  dmccooeyPropellor 480 360{4}+120{3} 422 12{10}+20{6}+390{4} 900 pkD
Propello Truncated Octahedron (canonical)  dmccooeyPropellor 96 72{4}+24{3} 86 8{6}+78{4} 180 ptO
Rectified Truncated Icosahedron  dmccooeyDerived 90 90{4} 92 20{6}+12{5}+60{3} 180
Regular Hexagonal Toroid with 10 faces (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 20 20{3} 10 10{6} 28
Regular Hexagonal Toroid with 11 faces  dmccooeyRegular Hexagonal Toroidalconcave 22 22{3} 11 11{6} 31
Regular Hexagonal Toroid with 12 faces (type A) (trapezohedral form)  dmccooeyRegular Hexagonal Toroidalconcave 24 24{3} 12 12{6} 34
Regular Hexagonal Toroid with 12 faces (type B)  dmccooeyRegular Hexagonal Toroidalconcave 24 24{3} 12 12{6} 34
Regular Hexagonal Toroid with 12 faces (type C) (knot form)  dmccooeyRegular Hexagonal Toroidalconcave 24 24{3} 12 12{6} 34
Regular Hexagonal Toroid with 12 faces (type C) (simple form)  dmccooeyRegular Hexagonal Toroidalconcave 24 24{3} 12 12{6} 34
Regular Hexagonal Toroid with 12 faces (type D) (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 24 24{3} 12 12{6} 34
Regular Hexagonal Toroid with 13 faces (type A)  dmccooeyRegular Hexagonal Toroidalconcave 26 26{3} 13 13{6} 37
Regular Hexagonal Toroid with 13 faces (type B) (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 26 26{3} 13 13{6} 37
Regular Hexagonal Toroid with 14 faces (type A) (version 2)  dmccooeyRegular Hexagonal Toroidalconcave 28 28{3} 14 14{6} 40
Regular Hexagonal Toroid with 14 faces (type B)  dmccooeyRegular Hexagonal Toroidalconcave 28 28{3} 14 14{6} 40
Regular Hexagonal Toroid with 15 faces (type A) (knot form 2)  dmccooeyRegular Hexagonal Toroidalconcave 30 30{3} 15 15{6} 43
Regular Hexagonal Toroid with 15 faces (type A) (version 1)  dmccooeyRegular Hexagonal Toroidalconcave 30 30{3} 15 15{6} 43
Regular Hexagonal Toroid with 15 faces (type D) (version 6)  dmccooeyRegular Hexagonal Toroidalconcave 30 30{3} 15 15{6} 43
Regular Hexagonal Toroid with 24 faces  dmccooeyRegular Hexagonal Toroidalconcave 48 48{3} 24 24{6} 70
Regular Hexagonal Toroid with 8 faces (D2 symmetry)  dmccooeyRegular Hexagonal Toroidalconcave 16 16{3} 8 8{6} 22
Regular Hexagonal Toroid with 8 faces (version 1)  dmccooeyRegular Hexagonal Toroidalconcave 16 16{3} 8 8{6} 22
Regular Hexagonal Toroid with 9 faces (type A) (cubic form)  dmccooeyRegular Hexagonal Toroidalconcave 18 18{3} 9 9{6} 25
Regular Hexagonal Toroid with 9 faces (type A) (triangular form)  dmccooeyRegular Hexagonal Toroidalconcave 18 18{3} 9 9{6} 25
Regular Hexagonal Toroid with 9 faces (type B)  dmccooeyRegular Hexagonal Toroidalconcave 18 18{3} 9 9{6} 25
Regular Map {4,6}10 (Schulte & Wills)  dmccooeyHigher Genus Toroidalconcave 20 20{6} 30 30{4} 48
Regular Map {6,4}10 (Schulte & Wills)  dmccooeyHigher Genus Toroidalconcave 30 30{4} 20 20{6} 48
Regular Tetragonal Toroid with 18 faces (type A) (version 1)  dmccooeyRegular Tetragonal Toroidalconcave 18 18{4} 18 18{4} 34
Regular Tetragonal Toroid with 18 faces (type A) (version 2)  dmccooeyRegular Tetragonal Toroidalconcave 18 18{4} 18 18{4} 34
Regular Tetragonal Toroid with 18 faces (type B) (antiprismatic form)  dmccooeyRegular Tetragonal Toroidalconcave 18 18{4} 18 18{4} 34
Regular Tetragonal Toroid with 18 faces (type B) (cubic form)  dmccooeyRegular Tetragonal Toroidalconcave 18 18{4} 18 18{4} 34
Regular Tetragonal Toroid with 9 faces  dmccooeyRegular Tetragonal Toroidalconcave 9 9{4} 9 9{4} 16
Regular Triangular Toroid with 16 faces  dmccooeyRegular Triangular Toroidalconcave 8 8{6} 16 16{3} 22
Regular Triangular Toroid with 18 faces (type A) (triangular form)  dmccooeyRegular Triangular Toroidalconcave 9 9{6} 18 18{3} 25
Regular Triangular Toroid with 18 faces (type B)  dmccooeyRegular Triangular Toroidalconcave 9 9{6} 18 18{3} 25
Regular Triangular Toroid with 20 faces  dmccooeyRegular Triangular Toroidalconcave 10 10{6} 20 20{3} 28
Regular Triangular Toroid with 22 faces  dmccooeyRegular Triangular Toroidalconcave 11 11{6} 22 22{3} 31
Regular Triangular Toroid with 24 faces (type A) (square form)  dmccooeyRegular Triangular Toroidalconcave 12 12{6} 24 24{3} 34
Regular Triangular Toroid with 24 faces (type B)  dmccooeyRegular Triangular Toroidalconcave 12 12{6} 24 24{3} 34
Regular Triangular Toroid with 24 faces (type C)  dmccooeyRegular Triangular Toroidalconcave 12 12{6} 24 24{3} 34
Regular Triangular Toroid with 24 faces (type D)  dmccooeyRegular Triangular Toroidalconcave 12 12{6} 24 24{3} 34
Rhombic Dodecahedron  dmccooeyCatalanisohedron 14 6{4}+8{3} 12 12{4} 24 jC
Rhombic Dodecahedron  Geodesic Cube Pattern 1 [1,1] dmccooeyGeodesic CubesSpace-fillingisotoxal 14 6{4}+8{3} 12 12{4} 24 jC
Rhombic Enneacontahedron  dmccooeyOther 92 20{6}+60{3}+12{5} 90 90{4} 180
Rhombic Hexecontahedron  Otherdmccooey 62 30{4}+20{3}+12{5} 60 60{4} 120
Rhombic Icosahedron  dmccooeyOther 22 10{4}+10{3}+2{5} 20 20{4} 40
Rhombic Triacontahedron  dmccooeyCatalanisohedron 32 12{5}+20{3} 30 30{4} 60 gD
Rhombicosacron  dmccooeyVersi-Quasi-Regular Dualsconcave 50 20{6}+30{4} 60 60{4} 108
Rhombicosahedron  dmccooeyVersi-Quasi-Regularconcave 60 60{4} 50 20{6}+30{4} 108
Rhombicosidodecahedron  dmccooeyArchimedean 60 60{4} 62 12{5}+30{4}+20{3} 120 aaD
Rhombicuboctahedron  dmccooeyArchimedean 24 24{4} 26 18{4}+8{3} 48 eO, eC, aaC
Rhombidodecadodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 54 24{5}+30{4} 112
Schönhardt Polyhedron  dmccooeyconcaveOther 6 6{4} 8 8{3} 12
Self-Dual Icosioctahedron #1 (canonical)  dmccooeyGreater Self-Dual 28 12{4}+12{3}+4{6} 28 4{6}+12{4}+12{3} 54
Self-Dual Icosioctahedron #2 (canonical)  dmccooeyGreater Self-Dual 28 12{5}+16{3} 28 12{5}+16{3} 54
Self-Dual Icosioctahedron #3 (canonical)  dmccooeyGreater Self-Dual 28 12{5}+16{3} 28 12{5}+16{3} 54
Self-Dual Icosioctahedron #4 (canonical)  dmccooeyGreater Self-Dual 28 24{4}+4{3} 28 24{4}+4{3} 54
Self-Dual Tetracontahedron #1 (canonical)  dmccooeyGreater Self-Dual 40 12{4}+24{3}+4{9} 40 4{9}+12{4}+24{3} 78
Self-Dual Tetracontahedron #2 (canonical)  dmccooeyGreater Self-Dual 40 12{5}+24{3}+4{6} 40 4{6}+12{5}+24{3} 78
Self-Dual Tetracontahedron #3 (canonical)  dmccooeyGreater Self-Dual 40 12{6}+28{3} 40 12{6}+28{3} 78
Self-Dual Tetracontahedron #4 (canonical)  dmccooeyGreater Self-Dual 40 12{4}+16{3}+12{5} 40 12{5}+12{4}+16{3} 78
Self-Dual Tetracontahedron #5 (canonical)  dmccooeyGreater Self-Dual 40 12{4}+12{5}+16{3} 40 12{5}+12{4}+16{3} 78
Self-Dual Tetracontahedron #6 (canonical)  dmccooeyGreater Self-Dual 40 12{5}+16{3}+12{4} 40 12{5}+12{4}+16{3} 78
Small Cubicuboctahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 24 24{4} 20 6{8}+6{4}+8{3} 42
Small Ditrigonal Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12{10}+20{3}+12{5} 60 60{4} 102
Small Ditrigonal Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 44 12{10}+12{5}+20{3} 102
Small Ditrigonal Icosidodecahedron  dmccooeySelf-Intersecting Quasi-Regularconcave 20 20{6} 32 12{5}+20{3} 50
Small Dodecacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 44 12{10}+20{3}+12{5} 60 60{4} 102
Small Dodecahemicosahedron  dmccooeyVersi-Regularconcave 30 30{4} 22 10{6}+12{5} 50
Small Dodecahemidodecahedron  dmccooeyVersi-Regularconcave 30 30{4} 18 6{10}+12{5} 46 k(h=-0.94,fn=[3])aD
Small Dodecicosacron  dmccooeyVersi-Quasi-Regular Dualsconcave 32 12{10}+20{6} 60 60{4} 90
Small Dodecicosahedron  dmccooeyVersi-Quasi-Regularconcave 60 60{4} 32 12{10}+20{6} 90
Small Dodecicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 44 12{10}+12{5}+20{3} 102
Small Hexacronic Icositetrahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 20 6{8}+6{4}+8{3} 24 24{4} 42
Small Hexagonal Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 112 100{3}+12{5} 60 60{6} 170
Small Hexagrammic Hexecontahedron  dmccooeySelf-Intersecting Snub Quasi-Regular Dualsconcave 112 100{3}+12{5} 60 60{6} 170
Small Icosacronic Hexecontahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regular Dualsconcave 52 20{6}+12{5}+20{3} 60 60{4} 110
Small Icosicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 52 20{6}+12{5}+20{3} 110
Small Icosihemidodecahedron  dmccooeyVersi-Regularconcave 30 30{4} 26 6{10}+20{3} 54 k(5,h=0.5)aD
Small Retrosnub Icosicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{6} 112 12{5}+100{3} 170
Small Rhombidodecacron  dmccooeyVersi-Quasi-Regular Dualsconcave 42 12{10}+30{4} 60 60{4} 100
Small Rhombidodecahedron  dmccooeyVersi-Quasi-Regularconcave 60 60{4} 42 12{10}+30{4} 100
Small Rhombihexacron  dmccooeyVersi-Quasi-Regular Dualsconcave 18 6{8}+12{4} 24 24{4} 40
Small Rhombihexahedron  dmccooeyVersi-Quasi-Regularconcave 24 24{4} 18 6{8}+12{4} 40
Small Snub Icosicosidodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{6} 112 12{5}+100{3} 170
Small Stellapentakis Dodecahedron  dmccooeySelf-Intersecting Truncated Regular Dualsconcave 24 12{10}+12{5} 60 60{3} 82
Small Stellated Dodecahedron  Stellated Dodecahedron dmccooeyKepler-Poinsotconcave 12 12{5} 12 12{5} 22 k(h=1)D
Small Stellated Truncated Dodecahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60{3} 24 12{10}+12{5} 82
Small Triambic Icosahedron  dmccooeySelf-Intersecting Quasi-Regular Dualsconcave 32 20{3}+12{5} 20 20{6} 50
Snub Cube  dmccooeychiralArchimedean 24 24{5} 38 6{4}+32{3} 60 sC
Snub Dodecadodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{5} 84 24{5}+60{3} 142
Snub Dodecahedron  dmccooeychiralArchimedean 60 60{5} 92 12{5}+80{3} 150 sD
Snub Hexpropello Dodecahedron (canonical)  dmccooeyDerived 420 420{5} 632 60{6}+12{5}+560{3} 1050 swD
Snub Icosidodecadodecahedron  dmccooeySelf-Intersecting Snub Quasi-Regularconcave 60 60{6} 104 24{5}+80{3} 162
Snub Truncated Icosahedron (canonical)  dmccooeyDerived 180 180{5} 272 20{6}+12{5}+240{3} 450 stI
Snub Truncated Octahedron (canonical)  dmccooeyDerived 72 72{5} 110 8{6}+6{4}+96{3} 180 stO
Square Antiprism  dmccooeyAntiprisms 8 8{4} 10 2{4}+8{3} 16 A4
Square Antiprism-Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 16 8{5}+8{3} 16 8{5}+8{3} 30
Square Dipyramid  Octahedron dmccooeyDipyramids and Trapezohedra 6 6{4} 8 8{3} 12 dP4
Square Prism (Cube)  dmccooeyPrisms 8 8{3} 6 6{4} 12 P4
Stella Octangula  Stellated Octahedron, Tetrahedron-Tetrahedron Compound dmccooeyconcaveOther 8 8{3} 8 8{3} 14 y0.65O
Stellated Truncated Hexahedron  dmccooeySelf-Intersecting Truncated Regularconcave 24 24{3} 14 6{8}+8{3} 36
Stewart's G3  dmccooeyconcaveOther 13 7{3}+3{4}+3{5} 13 3{5}+3{4}+7{3} 24
Szilassi Polyhedron (version 1)  dmccooeyRegular Hexagonal Toroidalconcave 14 14{3} 7 7{6} 19
Tetracontahedron with equal edges  dmccooeyOther 28 24{5}+4{3} 40 12{4}+28{3} 66
Tetradyakis Hexahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 20 12{8}+8{6} 48 48{3} 66
Tetragonal Trapezohedron  dmccooeyDipyramids and Trapezohedra 10 2{4}+8{3} 8 8{4} 16 dA4
Tetragonal Trapezohedron Toroid  dmccooeyNon-Regular Toroidalconcave 24 8{4}+16{3} 16 16{5} 38
Tetragonal Trapezohedron-Antiprism Toroid  dmccooeyNon-Regular Toroidalconcave 16 8{5}+8{3} 16 8{5}+8{3} 30
Tetrahedron  dmccooeyPlatonicisohedrondeltahedronisotoxal 4 4{3} 4 4{3} 6 T, Y3
Tetrahemihexahedron  dmccooeyVersi-Regularconcave 6 6{4} 7 3{4}+4{3} 11
Tetrakis Cuboctahedron (canonical)  dmccooeyDerived 18 6{4}+12{6} 32 32{3} 48 k4aC
Tetrakis Hexahedron  tetrahexahedron dmccooeyCatalanisohedron 14 6{4}+8{6} 24 24{3} 36 kC
Tetrakis Snub Cube (laevo) (canonical)  dmccooeyDerived 30 6{4}+24{6} 56 56{3} 84
Toroid with regular faces  dmccooeyNon-Regular Toroidalconcave 30 15{3}+12{4}+3{5} 24 9{6}+9{4}+6{3} 52
Triakis Icosahedron  dmccooeyCatalanisohedron 32 12{10}+20{3} 60 60{3} 90 kI
Triakis Octahedron  Small Triakis Octahedron, trisoctahedron dmccooeyCatalanisohedron 14 6{8}+8{3} 24 24{3} 36 kO
Triakis Tetrahedron  Tristetrahedron dmccooeyCatalanisohedron 8 4{6}+4{3} 12 12{3} 18 kT
Triangular Antiprism  Octahedron dmccooeyAntiprisms 6 6{4} 8 8{3} 12 A3
Triangular Dipyramid  dmccooeyDipyramids and Trapezohedra 5 2{3}+3{4} 6 6{3} 9 dP3
Triangular Prism  dmccooeyPrismsSpace-filling 6 6{3} 5 3{4}+2{3} 9 P3
Tridyakis Icosahedron  dmccooeySelf-Intersecting Truncated Quasi-Regular Dualsconcave 44 24{10}+20{6} 120 120{3} 162
Trigonal Trapezohedron  Cube dmccooeyDipyramids and Trapezohedra 8 8{3} 6 6{4} 12 dA3
Truncated Cube  dmccooeyArchimedean 24 24{3} 14 6{8}+8{3} 36 tC
Truncated Cuboctahedron  Great Rhombicuboctahedron dmccooeyArchimedean 48 48{3} 26 6{8}+8{6}+12{4} 72 NtaC
Truncated Disdyakis Dodecahedron  dmccooeyTruncated Catalan 144 144{3} 74 6{8}+56{6}+12{4} 216 tmC
Truncated Disdyakis Triacontahedron  dmccooeyTruncated Catalan 360 360{3} 182 12{10}+140{6}+30{4} 540 tMD
Truncated Dodecadodecahedron  dmccooeySelf-Intersecting Truncated Quasi-Regularconcave 120 120{3} 54 24{10}+30{4} 172
Truncated Dodecahedron  dmccooeyArchimedean 60 60{3} 32 12{10}+20{3} 90 tD
Truncated Great Dodecahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60{3} 24 12{10}+12{5} 82
Truncated Great Icosahedron  dmccooeySelf-Intersecting Truncated Regularconcave 60 60{3} 32 20{6}+12{5} 90
Truncated Icosahedron  Goldberg(1,1), Soccer Ball, C60 Buckyball dmccooeyGoldbergArchimedean 60 60{3} 32 20{6}+12{5} 90 tI
Truncated Icosidodecahedron  Great Rhombicosidodecahedron dmccooeyArchimedean 120 120{3} 62 12{10}+20{6}+30{4} 180 bD
Truncated Octahedron  dmccooeyArchimedean 24 24{3} 14 8{6}+6{4} 36 tO
Truncated Pentakis Dodecahedron (canonical)  Goldberg(3,0) dmccooeyGoldbergTruncated CatalanGoldberg 180 180{3} 92 80{6}+12{5} 270 tkD
Truncated Tetrahedron  dmccooeyArchimedean 12 12{3} 8 4{6}+4{3} 18 tT
Truncated Tetrakis Hexahedron (canonical)  dmccooeyTruncated Catalan 72 72{3} 38 32{6}+6{4} 108 tkC
Uniform Great Rhombicosidodecahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 60 60{4} 62 12{5}+30{4}+20{3} 120
Uniform Great Rhombicuboctahedron  dmccooeySelf-Intersecting Quasi-Quasi-Regularconcave 24 24{4} 26 18{4}+8{3} 48