Dodecahedron atop small rhombicosidodecahedron
Dodecahedron atop small rhombicosidodecahedron | |
---|---|
Rank | 4 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Doasrid |
Coxeter diagram | xx5oo3ox&#x |
Elements | |
Cells | 20 tetrahedra, 30 triangular prisms, 12 pentagonal prisms, 1 dodecahedron, 1 small rhombicosidodecahedron |
Faces | 20+60 triangles, 30+60 squares, 12+12 pentagons |
Edges | 30+60+60+60 |
Vertices | 20+60 |
Vertex figures | 20 triangular antipodiums, edge lengths 1 (base 1), √2 (sides), and (1+√5)/2 (base 2) |
60 isosceles trapezoidal pyramids, base edge lengths 1, √2, (1+√5)/2, √2, side edge lengths 1, 1, √2. √2 | |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Tet–3–trip: |
Pip–4–trip: | |
Doe–5–pip: 162° | |
Srid–3–tet: | |
Srid–4–trip: | |
Srid–5–pip: 18° | |
Height | |
Central density | 1 |
Related polytopes | |
Army | Doasrid |
Regiment | Doasrid |
Dual | Icosahedral-deltoidal hexecontahedral tegmoid |
Conjugate | Great stellated dodecahedron atop quasirhombicosidodecahedron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | H3×I, order 120 |
Convex | Yes |
Nature | Tame |
Dodecahedron atop small rhombicosidodecahedron, or doasrid, is a CRF segmentochoron (designated K-4.152 on Richard Klitzing's list). As the name suggests, it consists of a dodecahedron and a small rhombicosidodecahedron as bases, connected by 20 tetrahedra, 30 triangular prisms, and 12 pentagonal prisms.
It is also sometimes referred to as a dodecahedral cupola, as one generalization of the definition of a cupola is to have a polytope atop an expanded version.
It can be obtained as a dodecahedron-first cap of the small disprismatohexacosihecatonicosachoron.
Segmentochoron display[edit | edit source]
Vertex coordinates[edit | edit source]
The vertices of a dodecahedron atop small rhombicosidodecahedron segmentochoron of edge length 1 are given by all permutations of the first three coordinates of:
Plus all even permutations of:
External links[edit | edit source]
- Klitzing, Richard. "doasrid".
- Wikipedia contributors. "Dodecahedral cupola".