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Object in 4-dimensional geometry From Wikipedia, the free encyclopedia
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]
This article relies largely or entirely on a single source. (April 2024) |
Octahedral cupola | ||
---|---|---|
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 |
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) |
---|---|---|
B3 Coxeter plane | ||
B2 Coxeter plane | ||
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