### 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. Search

Name Groups #Vertices Vertex orders #Faces Face orders #Edges Conway
Chamfered Truncated Icosahedron (canonical)  Goldberg(2,2) dmccooeyChamferedGoldberg 240 240{3} 122 110{6}+12{5} 360 ctI
Dodecahedron  Goldberg(0,1) dmccooeyGoldbergPlatonicisohedronisotoxal 20 20{3} 12 12{5} 30 D, gY3
Dual Geodesic Icosahedron Pattern [16,0]  Goldberg(16,0) Dual Geodesic IcosahedraGoldberg 5120 2662 12{5}+2550{6} 7780 ccccD
Dual Geodesic Icosahedron Pattern [6,6]  Goldberg(6,6) Dual Geodesic IcosahedraGoldberg 2160 1082 12{5}+1070{6} 3240 ctktI
Dual Geodesic Icosahedron Pattern [9,0]  Goldberg(9,0) Dual Geodesic IcosahedraGoldberg 1620 812 12{5}+800{6} 2430 tdtdtkD
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
Truncated Icosahedron  Goldberg(1,1), Soccer Ball, C60 Buckyball dmccooeyGoldbergArchimedean 60 60{3} 32 20{6}+12{5} 90 tI
Truncated Pentakis Dodecahedron (canonical)  Goldberg(3,0) dmccooeyGoldbergTruncated CatalanGoldberg 180 180{3} 92 80{6}+12{5} 270 tkD