Cubic cupola
In 4-dimensional geometry, the cubic cupola is a 4-polytope bounded by a rhombicuboctahedron, a parallel cube, connected by 6 square prisms, 12 triangular prisms, 8 triangular pyramids.[1]
| Cubic cupola | ||
|---|---|---|
 Schlegel diagram | ||
| Type | Polyhedral cupola | |
| Schläfli symbol | {4,3} v rr{4,3} | |
| Cells | 28 | 1 rr{4,3}  1+6 {4,3}  12 {}×{3}  8 {3,3}  |
| Faces | 80 | 32 triangles 48 squares |
| Edges | 84 | |
| Vertices | 32 | |
| Dual | ||
| Symmetry group | [4,3,1], order 48 | |
| Properties | convex, regular-faced | |
Related polytopes
The cubic cupola can be sliced off from a runcinated tesseract, on a hyperplane parallel to cubic cell. The cupola can be seen in an edge-centered (B3) orthogonal projection of the runcinated tesseract:
| Runcinated tesseract | Cube (cupola top) |
Rhombicuboctahedron (cupola base) |
|---|---|---|
| B2 Coxeter plane | ||
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| B3 Coxeter plane | ||
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See also
- Cubic pyramid
- Octahedral cupola
- Runcinated tesseract
References
- Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.71 cube || rhombicuboctahedron)
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