Icosidodecatruncated icosidodecahedron
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Icosidodecatruncated icosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Idtid |
Coxeter diagram | x5/3x3x5*a () |
Elements | |
Faces | 20 hexagons, 12 decagons, 12 decagrams |
Edges | 60+60+60 |
Vertices | 120 |
Vertex figure | Scalene triangle, edge lengths √3, √(5+√5)/2, √(5–√5)/2 |
Measures (edge length 1) | |
Circumradius | 2 |
Volume | 80 |
Dihedral angles | 10/3–6: |
10–10/3: | |
10–6: | |
Central density | 4 |
Number of external pieces | 152 |
Level of complexity | 15 |
Related polytopes | |
Army | Semi-uniform Grid, edge lengths (decagons), 1 (ditrigon-rectangle) |
Regiment | Idtid |
Dual | Tridyakis icosahedron |
Conjugate | Icosidodecatruncated icosidodecahedron |
Convex core | Dodecahedron |
Abstract & topological properties | |
Flag count | 720 |
Euler characteristic | -16 |
Orientable | Yes |
Genus | 9 |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
The icosidodecatruncated icosidodecahedron or idtid, also called the icositruncated dodecadodecahedron, is a uniform polyhedron. It consists of 12 decagrams, 12 decagons, and 20 hexagons, with one of each type of face meeting per vertex.
It can be alternated into the snub icosidodecadodecahedron after equalizing edge lengths.
Vertex coordinates[edit | edit source]
An icosidodecatruncated icosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
Related polyhedra[edit | edit source]
Name | OBSA | CD diagram | Picture |
---|---|---|---|
Ditrigonary dodecadodecahedron | ditdid | ||
Small complex icosidodecahedron (degenerate, ike+gad) | cid | ||
Great complex icosidodecahedron (degenerate, sissid+gike) | gacid | ||
Icosidodecadodecahedron | ided | ||
Small ditrigonal dodecicosidodecahedron | sidditdid | ||
Great ditrigonal dodecicosidodecahedron | gidditdid | ||
Icosidodecatruncated icosidodecahedron | idtid | ||
Snub icosidodecadodecahedron | sided |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 5: Omnitruncates" (#63).
- Klitzing, Richard. "idtid".
- Wikipedia contributors. "Icositruncated dodecadodecahedron".
- McCooey, David. "Icositruncated Dodecadodecahedron"