Dodecahedral cupola
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| Dodecahedral cupola | ||
|---|---|---|
| File:Dodecahedral cupola.png Schlegel diagram | ||
| Type | Polyhedral cupola | |
| Schläfli symbol | {5,3} v rr{5,3} | |
| Cells | 64 | 1 rr{5,3} File:Uniform polyhedron-53-t02.png 1 {5,3} File:Uniform polyhedron-53-t0.png 30 {}×{3} File:Triangular prism.png 12 {}×{5} File:Pentagonal prism.png 20 {3,3} File:Uniform polyhedron-33-t0.png |
| Faces | 194 | 80 triangles 90 squares 24 pentagons |
| Edges | 210 | |
| Vertices | 80 | |
| Dual | ||
| Symmetry group | [5,3,1], order 120 | |
| Properties | convex, regular-faced | |
In 4-dimensional geometry, the dodecahedral cupola is a polychoron bounded by a rhombicosidodecahedron, a parallel dodecahedron, connected by 30 triangular prisms, 12 pentagonal prisms, and 20 tetrahedra.[1]
Related polytopes
The dodecahedral cupola can be sliced off from a runcinated 120-cell, on a hyperplane parallel to a dodecahedral cell. The cupola can be seen in a pentagonal centered orthogonal projection of the runcinated 120-cell:
| Runcinated 120-cell File:120-cell t03 H3.png |
Dodecahedron File:Dodecahedron H3 projection.svg (cupola top) |
| Rhombicosidodecahedron File:Dodecahedron t02 H3.png (cupola base) |
See also
References
- ↑ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.152 dodecahedron || rhombicosidodecahedron)
External links
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