User:The Nth User/Extended Archimedean solid table
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Symmetry | Triangular dihedral symmetry |
Tetrahedral |
Octahedral |
Icosahedral |
p6m symmetry |
[3,7] symmetry |
[3,8] symmetry | |||||||
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Starting solid Operation |
Symbol {p,q} |
Triangular hosohedron {2,3} |
Triangular dihedron {3,2} |
Tetrahedron {3,3} |
Cube {4,3} |
Octahedron {3,4} |
Dodecahedron {5,3} |
Icosahedron {3,5} |
Hexagonal tiling {6,3} |
Triangular tiling {3,6} |
Heptagonal tiling {7,3} |
Order-7 triangular tiling {3,7} |
Octagonal tiling {8,3} |
Order-8 triangular tiling {3,8} |
Truncation (t) | t{p,q} |
triangular prism |
truncated triangular dihedron (Half of the "edges" count as degenerate digon faces. The other half are normal edges.) |
truncated tetrahedron |
truncated cube |
truncated octahedron |
truncated dodecahedron |
truncated icosahedron |
Truncated hexagonal tiling |
Truncated triangular tiling |
Truncated heptagonal tiling |
Truncated order-7 triangular tiling |
Truncated octagonal tiling |
Truncated order-8 triangular tiling |
Rectification (r) Ambo (a) |
r{p,q} |
tridihedron (All of the "edges" count as degenerate digon faces.) |
tetratetrahedron |
cuboctahedron |
icosidodecahedron |
Trihexagonal tiling |
Triheptagonal tiling |
Trioctagonal tiling | ||||||
Bitruncation (2t) Dual kis (dk) |
2t{p,q} |
truncated triangular dihedron (Half of the "edges" count as degenerate digon faces. The other half are normal edges.) |
triangular prism |
truncated tetrahedron |
truncated octahedron |
truncated cube |
truncated icosahedron |
truncated dodecahedron |
truncated triangular tiling |
truncated hexagonal tiling |
Truncated order-7 triangular tiling |
Truncated heptagonal tiling |
Truncated order-8 triangular tiling |
Truncated octagonal tiling |
Birectification (2r) Dual (d) |
2r{p,q} |
triangular dihedron {3,2} |
triangular hosohedron {2,3} |
tetrahedron |
octahedron |
cube |
icosahedron |
dodecahedron |
triangular tiling |
hexagonal tiling |
Order-7 triangular tiling |
Heptagonal tiling |
Order-8 triangular tiling |
Octagonal tiling |
Cantellation (rr) Expansion (e) |
rr{p,q} |
triangular prism (The "edge" between each pair of tetragons counts as a degenerate digon face. The other edges (the ones between a trigon and a tetragon) are normal edges.) |
rhombitetratetrahedron |
rhombicuboctahedron |
rhombicosidodecahedron |
rhombitrihexagonal tiling |
Rhombitriheptagonal tiling |
Rhombitrioctagonal tiling | ||||||
Snub rectified (sr) Snub (s) |
sr{p,q} |
triangular antiprism (Three yellow-yellow "edges", no two of which share any vertices, count as degenerate digon faces. The other edges are normal edges.) |
snub tetratetrahedron |
snub cuboctahedron |
snub icosidodecahedron |
snub trihexagonal tiling |
Snub triheptagonal tiling |
Snub trioctagonal tiling | ||||||
Cantitruncation (tr) Bevel (b) |
tr{p,q} |
hexagonal prism |
truncated tetratetrahedron |
truncated cuboctahedron |
truncated icosidodecahedron |
truncated trihexagonal tiling |
Truncated triheptagonal tiling |
Truncated trioctagonal tiling |