Tetrahedral cupola

Tetrahedral cupola

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]

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
Runcinated 5-cell Tetrahedron
(Cupola top)		 Cuboctahedron
(Cupola base)
A2 Coxeter plane

See also

References

  1. ↑ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.23 tetrahedron || cuboctahedron)
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