Icosidodecadodecahedron
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Icosidodecadodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Ided |
Coxeter diagram | o5/3x3x5*a () |
Elements | |
Faces | 12 pentagons, 12 pentagrams, 20 hexagons |
Edges | 60+60 |
Vertices | 60 |
Vertex figure | Crossed isosceles trapezoid, edge lengths (√5–1)/2, √3, (1+√5)/2, √3 |
Measures (edge length 1) | |
Circumradius | |
Volume | 20 |
Dihedral angles | 5–6: |
5/2–6: | |
Central density | 4 |
Number of external pieces | 408 |
Level of complexity | 25 |
Related polytopes | |
Army | Semi-uniform ti, edge lengths (pentagons), (between ditrigons) |
Regiment | Raded |
Dual | Medial icosacronic hexecontahedron |
Conjugate | Icosidodecadodecahedron |
Convex core | Truncated icosahedron |
Abstract & topological properties | |
Flag count | 480 |
Euler characteristic | –16 |
Orientable | Yes |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
The icosidodecadodecahedron, or ided, is a uniform polyhedron. It consists of 12 pentagons, 12 pentagrams, and 20 hexagons. One pentagon, one pentagram, and two hexagons join at each vertex.
It is a faceting of the rhombidodecadodecahedron, using its 12 pentagrams and 12 pentagons along with 20 additional hexagons.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the rhombidodecadodecahedron.
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 4: Trapeziverts" (#43).
- Klitzing, Richard. "ided".
- Wikipedia Contributors. "Icosidodecadodecahedron".
- McCooey, David. "Icosidodecadodecahedron"