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 dodecagonal 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

  1. 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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