This article relies largely or entirely on a single source. (April 2024) |
Tetrahedral cupola | ||
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![]() Schlegel diagram | ||
Type | Polyhedral cupola | |
Schläfli symbol | {3,3} v rr{3,3} | |
Cells | 16 | 1 rr{3,3} ![]() 1+4 {3,3} ![]() 4+6 {}×{3} ![]() |
Faces | 42 | 24 triangles 18 squares |
Edges | 42 | |
Vertices | 16 | |
Dual | ||
Symmetry group | [3,3,1], order 24 | |
Properties | convex, regular-faced |
In 4-dimensional geometry, the tetrahedral cupola is a polychoron bounded by one tetrahedron, a parallel cuboctahedron, connected by 10 triangular prisms, and 4 triangular pyramids.[1]
Related polytopes
The tetrahedral cupola can be sliced off from a runcinated 5-cell, on a hyperplane parallel to a tetrahedral cell. The cuboctahedron base passes through the center of the runcinated 5-cell, so the Tetrahedral cupola contains half of the tetrahedron and triangular prism cells of the runcinated 5-cell. The cupola can be seen in A2 and A3 Coxeter plane orthogonal projection of the runcinated 5-cell:
A3 Coxeter plane | ||
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Runcinated 5-cell | Tetrahedron (Cupola top) |
Cuboctahedron (Cupola base) |
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A2 Coxeter plane | ||
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See also
- Tetrahedral pyramid (5-cell)
References
- ^ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.23 tetrahedron || cuboctahedron)
External links