User:The Nth User/Extended Archimedean solid table
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More information Symmetry, Triangular dihedral symmetry ...
Symmetry | Triangular dihedral symmetry |
Tetrahedral |
Octahedral |
Icosahedral |
p6m symmetry |
[3,7] symmetry |
[3,8] symmetry | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 |
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