Octahedral cupola Contents Related polytopes See also References External links Navigation menuConvex SegmentochoraSegmentochora:oct || sirco, K-4.107expanding ite

PolychoraPolychora stubs


geometry4-polytopeoctahedronrhombicuboctahedrontriangular prismssquare pyramidsruncinated 24-cell
























Octahedral cupola

4D octahedral cupola-perspective-octahedron-first.png
Schlegel diagram
Type

Polyhedral cupola

Schläfli symbol
3,4 v rr3,4
Cells
28
1 3,4 Uniform polyhedron-43-t2.png
1 rr4,3 Uniform polyhedron-43-t02.png
8+12 ×3 Triangular prism.png
6 v4 Square pyramid.png
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]




Contents





  • 1 Related polytopes


  • 2 See also


  • 3 References


  • 4 External links




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

24-cell t03 B3.svg
3-cube t2.svg
3-cube t02.svg
B2 Coxeter plane

24-cell t03 B2.svg
3-cube t2 B2.svg
3-cube t02 B2.svg


See also


  • Octahedral pyramid

  • Cubic cupola

  • Runcinated 24-cell


References




  1. ^ Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.107 octahedron || rhombicuboctahedron)




External links



  • Segmentochora: oct || sirco, K-4.107






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