Icosidodecadodecahedron
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.
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 |
It is a faceting of the rhombidodecadodecahedron, using its 12 pentagrams and 12 pentagons along with 20 additional hexagons.
Vertex coordinatesEdit
Its vertices are the same as those of its regiment colonel, the rhombidodecadodecahedron.
Related polyhedraEdit
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 linksEdit
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#43).
- Klitzing, Richard. "ided".
- Wikipedia Contributors. "Icosidodecadodecahedron".
- McCooey, David. "Icosidodecadodecahedron"