Octahedral cupola
Octahedral cupola | ||
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![]() Schlegel diagram | ||
Type | Polyhedral cupola | |
Schläfli symbol | {3,4} v rr{3,4} | |
Cells | 28 | 1 {3,4} ![]() 1 rr{4,3} ![]() 8+12 {}×{3} ![]() 6 {}v{4} ![]() |
Faces | 82 | 40 triangles 42 squares |
Edges | 84 | |
Vertices | 30 | |
Dual | ||
Symmetry group | [4,3,1], order 48 | |
Properties | convex, regular-faced |
In 4-dimensional geometry, the octahedral cupola is a 4-polytope bounded by one octahedron and a parallel rhombicuboctahedron, connected by 20 triangular prisms, and 6 square pyramids.[1]
Related polytopes[]
The octahedral cupola can be sliced off from a runcinated 24-cell, on a hyperplane parallel to an octahedral cell. The cupola can be seen in a B2 and B3 Coxeter plane orthogonal projection of the runcinated 24-cell:
Runcinated 24-cell | Octahedron (cupola top) |
Rhombicuboctahedron (cupola base) |
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B3 Coxeter plane | ||
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B2 Coxeter plane | ||
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See also[]
- Octahedral pyramid
- Cubic cupola
- Runcinated 24-cell
References[]
- ^ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.107 octahedron || rhombicuboctahedron)
External links[]
Categories:
- 4-polytopes
- Four-dimensional geometry
- 4-polytopes stubs