Octahedral cupola

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Octahedral cupola
4D octahedral cupola-perspective-octahedron-first.png
Schlegel diagram
Type Polyhedral cupola
Schläfli symbol {3,4} v rr{3,4}
Cells281 {3,4} Uniform polyhedron-43-t2.svg
1 rr{4,3} Uniform polyhedron-43-t02.png
8+12 {}×{3} Triangular prism.png
6 {}v{4} Square pyramid.png
Faces8240 triangles
42 squares
Edges84
Vertices30
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]

Contents

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
24-cell t03 B3.svg 3-cube t2.svg 3-cube t02.svg
B2 Coxeter plane
24-cell t03 B2.svg 3-cube t2 B2.svg 3-cube t02 B2.svg

See also

References

  1. ↑ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.107 octahedron || rhombicuboctahedron)


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