Truncated great dodecahedron
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Truncated great dodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Tigid |
Coxeter diagram | o5/2x5x () |
Elements | |
Faces | 12 pentagrams, 12 decagons |
Edges | 30+60 |
Vertices | 60 |
Vertex figure | Isosceles triangle, edge lengths (√5–1)/2, √(5+√5)/2, √(5+√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 10–5/2: |
10–10: | |
Central density | 3 |
Number of external pieces | 72 |
Level of complexity | 7 |
Related polytopes | |
Army | Semi-uniform Ti, edge lengths (pentagons) and 1 (between ditrigons) |
Regiment | Tigid |
Dual | Small stellapentakis dodecahedron |
Conjugate | Quasitruncated small stellated dodecahedron |
Convex core | Dodecahedron |
Abstract & topological properties | |
Flag count | 360 |
Euler characteristic | -6 |
Orientable | Yes |
Genus | 4 |
Properties | |
Symmetry | H3, order 120 |
Convex | No |
Nature | Tame |
The truncated great dodecahedron, or tigid, also called the great truncated dodecahedron, is a uniform polyhedron. It consists of 12 pentagrams and 12 decagons. Each vertex joins one pentagram and two decagons. As the name suggests, it can be obtained by the truncation of the great dodecahedron.
Vertex coordinates[edit | edit source]
A truncated great dodecahedron of edge length 1 has vertex coordinates given by all permutations of:
- ,
plus all even permutations of:
- ,
- .
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#15).
- Klitzing, Richard. "tigid".
- Wikipedia contributors. "Truncated great dodecahedron".
- McCooey, David. "Truncated Great Dodecahedron"