Polyhedra in OpenSCAD

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group : Goldberg   Count = 32
A Goldberg polyhedron is composed of pentagons and hexagons with all vertices of order 3 ( hence duals of Geodesic Icosahedra). A consequence of Euler's law is that there are always 12 pentagons. They can be charactised by the number of hexagons encountered on any dog-leg path between pentagons.
Some have Conway formula but many do not.
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Name Groups #Vertices Vertex orders #Faces Face orders #Edges Conway
Chamfered Truncated Icosahedron (canonical)  Goldberg(2,2) dmccooeyChamferedGoldberg 240 240 of 3 122 110 of 6,12 of 5 360 ctI
Dodecahedron  Goldberg(0,1) dmccooeyGoldbergPlatonicisohedron 20 20 of 3 12 12 of 5 30 D, gY3
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
Truncated Icosahedron  Goldberg(1,1), Soccer Ball, C60 Buckyball dmccooeyGoldbergArchimedean 60 60 of 3 32 20 of 6,12 of 5 90 tI
Truncated Pentakis Dodecahedron (canonical)  Goldberg(3,0) dmccooeyGoldbergTruncated CatalanGoldberg 180 180 of 3 92 80 of 6,12 of 5 270 tkD