Octahedral cupola
{{Short description|Object in 4-dimensional geometry}}
{{one source |date=April 2024}}
| class="wikitable" align="right" style="margin-left:10px" width="280" |
| bgcolor=#e7dcc3 colspan=3|Octahedral cupola |
|---|
| align=center colspan=3|280px Schlegel diagram |
| bgcolor=#e7dcc3|Type
|colspan=2|Polyhedral cupola |
| bgcolor=#e7dcc3|Schläfli symbol
|colspan=2|{3,4} v rr{3,4} |
| bgcolor=#e7dcc3|Cells
|28 |
| bgcolor=#e7dcc3|Faces
|82 |40 triangles |
| bgcolor=#e7dcc3|Edges
|colspan=2|84 |
| bgcolor=#e7dcc3|Vertices
|colspan=2|30 |
| bgcolor=#e7dcc3|Dual
|colspan=2| |
| bgcolor=#e7dcc3|Symmetry group
|colspan=2|[4,3,1], order 48 |
| bgcolor=#e7dcc3|Properties
|colspan=2|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.[https://www.bendwavy.org/klitzing/pdf/artConvSeg_8.pdf Convex Segmentochora] Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.107 octahedron || rhombicuboctahedron)
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:
| class=wikitable |
| align=center
!Runcinated 24-cell !Octahedron !Rhombicuboctahedron |
| colspan=3|B3 Coxeter plane |
|---|
| align=center
|60px |
| colspan=3|B2 Coxeter plane |
| align=center
|60px |
See also
References
{{reflist}}
External links
- [https://bendwavy.org/klitzing/explain/segmentochora.htm Segmentochora:] [https://bendwavy.org/klitzing/incmats/oct=sirco.htm oct || sirco, K-4.107]
Category:Four-dimensional geometry
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