Octahedral cupola explained

bgcolor=#e7dcc3 colspan=3	Octahedral cupola
align=center colspan=3	Schlegel diagram
Type	Polyhedral cupola
Schläfli symbol	v rr
Cells	28
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:

See also

• Octahedral pyramid
• Cubic cupola
• Runcinated 24-cell

External links

• Segmentochora: oct || sirco, K-4.107

Notes and References

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