Dodecahedral cupola
# Dodecahedral cupola

Dodecahedral cupola :

| Schlegel diagram |||
| - | - | - |
| Type | Polyhedral cupola | Polyhedral cupola |
| Schläfli symbol | {5,3} v rr{5,3} | {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 | 210 |
| Vertices | 80 | 80 |
| Dual | | |
| Symmetry group | [5,3,1], order 120 | [5,3,1], order 120 |
| Properties | convex, regular-faced | 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.

## 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) |
| - | - |
| Runcinated 120-cell | Rhombicosidodecahedron (cupola base) |
