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]
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) |