Tetrahedral cupola explained

bgcolor=#e7dcc3 colspan=3	Tetrahedral cupola
align=center colspan=3	Schlegel diagram
Type	Polyhedral cupola
Schläfli symbol	v rr
Cells	16
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:

See also

• Tetrahedral pyramid (5-cell)

External links

• Segmentochora: tetaco, tet || co, K-4.23

Notes and References

1. http://www.bendwavy.org/klitzing/pdf/artConvSeg_8.pdf Convex Segmentochora