Truncated great icosahedron
Jump to navigation
Jump to search
Truncated great icosahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Tiggy |
Coxeter diagram | o5/2x3x () |
Elements | |
Faces | 12 pentagrams, 20 hexagons |
Edges | 30+60 |
Vertices | 60 |
Vertex figure | Isosceles triangle, edge lengths (√5–1)/2, √3, √3 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 6–5/2: |
6–6: | |
Central density | 7 |
Number of external pieces | 192 |
Level of complexity | 13 |
Related polytopes | |
Army | Semi-uniform Srid, edge lengths 1 (pentagons) and (triangles) |
Regiment | Tiggy |
Dual | Great stellapentakis dodecahedron |
Conjugate | Truncated icosahedron |
Convex core | Icosahedron |
Abstract & topological properties | |
Flag count | 360 |
Euler characteristic | 2 |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
The truncated great icosahedron, or tiggy, also called the great truncated icosahedron, is a uniform polyhedron. It consists of 12 pentagrams and 20 hexagons. Each vertex joins one pentagram and two hexagons. As the name suggests, it can be obtained by the truncation of the great icosahedron.
Vertex coordinates[edit | edit source]
A truncated great icosahedron of edge length 1 has vertex coordinates given by all even permutations and all changes of sign of:
Related polyhedra[edit | edit source]
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Great icosahedron | gike | {3,5/2} | x3o5/2o () | |
Truncated great icosahedron | tiggy | t{3,5/2} | x3x5/2o () | |
Great icosidodecahedron | gid | r{3,5/2} | o3x5/2o () | |
Truncated great stellated dodecahedron (degenerate, ike+2gad) | t{5/2,3} | o3x5/2x () | ||
Great stellated dodecahedron | gissid | {5/2,3} | o3o5/2x () | |
Small complex rhombicosidodecahedron (degenerate, sidtid+rhom) | sicdatrid | rr{3,5/2} | x3o5/2x () | |
Truncated great icosidodecahedron (degenerate, ri+12(10/2)) | tr{3,5/2} | x3x5/2x () | ||
Great snub icosidodecahedron | gosid | sr{3,5/2} | s3s5/2s () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#16).
- Klitzing, Richard. "tiggy".
- Wikipedia Contributors. "Truncated great icosahedron".
- McCooey, David. "Truncated Great Icosahedron"