Octahedral cupola

Schlegel diagram
Type Polyhedral cupola
Schläfli symbol {3,4} v rr{3,4}
Cells 28 1 {3,4}
1 rr{4,3}
8+12 {}×{3}
6 {}v{4}
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]

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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
     
B2 Coxeter plane
     

See also

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References

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  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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