Dodecahedral cupola
Dodecahedral cupola | ||
---|---|---|
![]() Schlegel diagram | ||
Type | Polyhedral cupola | |
Schläfli symbol | {5,3} v rr{5,3} | |
Cells | 64 | 1 rr{5,3} ![]() 1 {5,3} ![]() 30 {}×{3} ![]() 12 {}×{5} ![]() 20 {3,3} ![]() |
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![]() |
Dodecahedron![]() (cupola top) |
Rhombicosidodecahedron![]() (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[]
Categories:
- 4-polytopes
- Four-dimensional geometry
- 4-polytopes stubs