tetrahedral cupola
{{one source |date=April 2024}}
| class="wikitable" align="right" style="margin-left:10px" width="280" |
| bgcolor=#e7dcc3 colspan=3|Tetrahedral cupola |
|---|
| align=center colspan=3|280px Schlegel diagram |
| bgcolor=#e7dcc3|Type
|colspan=2|Polyhedral cupola |
| bgcolor=#e7dcc3|Schläfli symbol
|colspan=2|{3,3} v rr{3,3} |
| bgcolor=#e7dcc3|Cells
|16 |
| bgcolor=#e7dcc3|Faces
|42 |24 triangles |
| bgcolor=#e7dcc3|Edges
|colspan=2|42 |
| bgcolor=#e7dcc3|Vertices
|colspan=2|16 |
| bgcolor=#e7dcc3|Dual
|colspan=2| |
| bgcolor=#e7dcc3|Symmetry group
|colspan=2|[3,3,1], order 24 |
| bgcolor=#e7dcc3|Properties
|colspan=2|convex, regular-faced |
In 4-dimensional geometry, the tetrahedral cupola is a polychoron bounded by one tetrahedron, a parallel cuboctahedron, connected by 10 triangular prisms, and 4 triangular pyramids.[http://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 (4.23 tetrahedron || cuboctahedron)
Related polytopes
The tetrahedral cupola can be sliced off from a runcinated 5-cell, on a hyperplane parallel to a tetrahedral cell. The cuboctahedron base passes through the center of the runcinated 5-cell, so the Tetrahedral cupola contains half of the tetrahedron and triangular prism cells of the runcinated 5-cell. The cupola can be seen in A2 and A3 Coxeter plane orthogonal projection of the runcinated 5-cell:
| class=wikitable
!colspan=3|A3 Coxeter plane |
| align=center
!Runcinated 5-cell !Tetrahedron !Cuboctahedron |
| align=center |
| colspan=3|A2 Coxeter plane |
|---|
| align=center |
See also
- Tetrahedral pyramid (5-cell)
References
{{reflist}}
External links
- [http://bendwavy.org/klitzing/explain/segmentochora.htm Segmentochora:] [http://bendwavy.org/klitzing/incmats/co=tet.htm tetaco, tet || co, K-4.23]
{{Polychora-stub}}