Octahedral cupola
From HandWiki
Short description: Object in 4-dimensional geometry
| Octahedral cupola | ||
|---|---|---|
 Schlegel diagram | ||
| Type | Polyhedral cupola | |
| Schläfli symbol | {3,4} v rr{3,4} | |
| Cells | 28 | 1 {3,4}  1 rr{4,3} 30px 8+12 {}×{3} 30px 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]
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:
| Runcinated 24-cell | Octahedron (cupola top) |
Rhombicuboctahedron (cupola base) |
|---|---|---|
| B3 Coxeter plane | ||
|
|
|
| B2 Coxeter plane | ||
|
|
|
See also
- Octahedral pyramid
- Cubic cupola
- Runcinated 24-cell
References
- ↑ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.107 octahedron || rhombicuboctahedron)
External links
 |  |
