Truncated great dodecahedron
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Truncated great dodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
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 pieces | 72 |
Level of complexity | 7 |
Related polytopes | |
Army | Semi-uniform Ti |
Regiment | Tigid |
Dual | Small stellapentakis dodecahedron |
Conjugate | Quasitruncated small stellated dodecahedron |
Convex core | Dodecahedron |
Abstract properties | |
Euler characteristic | -6 |
Topological properties | |
Orientable | Yes |
Genus | 4 |
Properties | |
Symmetry | H_{3}, 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:
Related polyhedra[edit | edit source]
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Great dodecahedron | gad | {5,5/2} | x5o5/2o () | |
Truncated great dodecahedron | tigid | t{5,5/2} | x5x5/2o () | |
Dodecadodecahedron | did | r{5,5/2} | o5x5/2o () | |
Truncated small stellated dodecahedron (degenerate, triple cover of doe) | t{5/2,5} | o5x5/2x () | ||
Small stellated dodecahedron | sissid | {5/2,5} | o5o5/2x () | |
Rhombidodecadodecahedron | raded | rr{5,5/2} | x5o5/2x () | |
Truncated dodecadodecahedron (degenerate, sird+12(10/2)) | tr{5,5/2} | x5x5/2x () | ||
Snub dodecadodecahedron | siddid | sr{5,5/2} | s5s5/2s () |
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"