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Platonic Solids

Tetrahedron Cube Octahedron Dodecahedron Icosahedron Stellated Dodecahedron Great Dodecahedron Great Stellated Dodecahedron Great Icosahedron Cuboctahedron Icosidodecahedron Truncated Tetrahedron Truncated Cube Truncated Octahedron Truncated Dodecahedron Truncated Icosahedron Rhombicuboctahedron Great Rhombicuboctahedron Rhombicosidodecahedron Great Rhombicosidodecahedron Snub Cube Snub Dodecahedron Vertices 4 8 6 20 12 12 12 20 12 12 30 12 24 24 60 60 24 48 60 120 24 60 Edges 6 12 12 30 30 30 30 30 30 24 60 18 36 36 90 90 48 72 120 180 60 150 Faces total 4 6 8 12 20 12 12 12 20 14 32 8 14 14 32 32 26 26 62 62 38 92 Symmetry Tetr. Oct. Oct. Icos. Icos. Icos. Icos. Icos. Icos. Oct. Icos. Tetr. Oct. Oct. Icos. Icos. Oct. Oct. Icos. Icos. Oct. Icos. data table Symmetries Tetrahedral 4 x 3fold axes, 3 x 2fold, 6 mirror planes. Octahedral 3 x 4fold axes, 4 x 3fold, 6 x 2fold, 9 mirror planes. Icosahedral 6 x 5fold axes, 10 x 3fold, 15 x 2fold, 15 mirror planes. The snub solids have no mirror planes. Inradius Circumradius 0.3333333333 0.5773502692 0.5773502692 0.7946544723 0.7946544723 0.4472135955 0.4472135955 0.1875924741 0.1875924741 0.8164965809 0.7071067812 0.9341723590 0.8506508084 0.8703882798 0.5222329679 0.9458621650 0.6785983445 0.8944271910 0.7745966692 0.9809163757 0.8385051474 0.9392336205 0.9149583817 0.9108680249 0.8628562095 0.9523198087 0.9021230715 0.8259425910 0.9659953695 0.9485360199 0.9245941063 0.9825566436 0.9647979663 0.9049441875 0.9029870683 0.8503402074 0.9634723304 0.9188614921 Midradius Circumradius 0.5773502692 0.8164965809 0.7071067812 0.9341723590 0.8506508084 0.5257311121 0.8506508084 0.3568220898 0.5257311121 0.8660254038 0.9510565163 0.9045340337 0.9596829823 0.9486832981 0.9857219193 0.9794320855 0.9339488311 0.9764509762 0.9746077624 0.9913166895 0.9281913780 0.9727328506 Edge Length Circumradius 1.6329931619 1.1547005384 1.4142135624 0.7136441795 1.0514622242 1.7013016167 1.0514622242 1.8683447179 1.7013016167 1.0000000000 0.6180339887 0.8528028654 0.5621692754 0.6324555320 0.3367628118 0.4035482123 0.7148134887 0.4314788105 0.4478379596 0.2629921751 0.7442063312 0.4638568806 Dihedral Angles 703144 900000 1092816 1163354 1381123 1163354 632606 632606 414837 1251552 1423721 703144 1092816 900000 1251552 1092816 1251552 1163354 1423721 1381123 1423721 1350000 1444408 1251552 1350000 1444408 1481657 1535633 1590541 1423721 1481657 1590541 1425900 1531405 1525548 1641031 Central Angle 1092816 703144 900000 414837 632606 1163354 632606 1381123 1163354 600000 360000 502844 323900 365212 192315 231653 415255 245504 255243 150644 434127 264917 From the polyhedrons centre the inradius is measured to the various facecentres, the midradius to the centres of edges and the circumradius to vertices. In Archimedean Solids the larger dihedral angles are found between smaller pairs of faces. The central angle is the angle formed at the centre of a polyhedron by joining the ends of an edge to that centre. Faces types 4 triangles 6 squares 8 triangles 12 pentagons 20 triangles 12 pentagrams 12 pentagons 12 pentagrams 20 triangles 8 triangles 6 squares 20 triangles 12 pentagons 4 triangles 4 hexagons 8 triangles 6 octagons 6 squares 8 hexagons 20 triangles 12 decagons 12 pentagons 20 hexagons 8 triangles 18 squares 12 squares 8 hexagons 6 octagons 20 triangles 30 squares 12 pentagons 30 squares 20 hexagons 12 decagons 32 triangles 6 squares 80 triangles 12 pentagons
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