Small ditrigonal dodecicosidodecahedron
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.
Small ditrigonal dodecicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
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 |
Convex | No |
Nature | Tame |
It is a faceting of the small icosicosidodecahedron, using its 12 pentagrams and 20 triangles along with 12 additional decagons.
Vertex coordinatesEdit
Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedron.
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" (#52).
- Klitzing, Richard. "sidditdid".
- Wikipedia Contributors. "Small ditrigonal dodecicosidodecahedron".
- McCooey, David. "Small Ditrigonal dodecicosidodecahedron"