Small ditrigonal dodecicosidodecahedron
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Small ditrigonal dodecicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Sidditdid |
Coxeter diagram | x5/3o3x5*a () |
Elements | |
Faces | 20 triangles, 12 pentagrams, 12 decagons |
Edges | 60+60 |
Vertices | 60 |
Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √(5+√5)/2, (√5–1)/2, √(5+√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 3–10: |
5/2–10: | |
Central density | 4 |
Number of external pieces | 212 |
Level of complexity | 13 |
Related polytopes | |
Army | Semi-uniform Srid, edge lengths (pentagons), 1 (triangles) |
Regiment | Siid |
Dual | Small ditrigonal dodecacronic hexecontahedron |
Conjugate | Great ditrigonal dodecicosidodecahedron |
Convex core | Dodecahedron |
Abstract & topological properties | |
Flag count | 480 |
Euler characteristic | –16 |
Orientable | Yes |
Properties | |
Symmetry | H_{3}, order 120 |
Flag orbits | 4 |
Convex | No |
Nature | Tame |
The small ditrigonal dodecicosidodecahedron, or sidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagons. One triangle, one pentagram, and two decagons join at each vertex.
It is a faceting of the small icosicosidodecahedron, using its 12 pentagrams and 20 triangles along with 12 additional decagons.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedron.
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" (#52).
- Klitzing, Richard. "sidditdid".
- Wikipedia contributors. "Small ditrigonal dodecicosidodecahedron".
- McCooey, David. "Small Ditrigonal dodecicosidodecahedron"