| 5-orthoplex honeycomb
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| (No image)
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| Type |
Hyperbolic regular honeycomb
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| Schläfli symbol |
{3,3,3,4,3}
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| Coxeter diagram |
File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel splitsplit1.pngFile:CDel branch3.pngFile:CDel node.png = File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node g.pngFile:CDel 3sg.pngFile:CDel node g.png
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| 5-faces |
File:5-cube t4.svg {3,3,3,4}
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| 4-faces |
File:Schlegel wireframe 5-cell.png {3,3,3}
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| Cells |
File:Tetrahedron.png {3,3}
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| Faces |
File:Regular polygon 3 annotated.svg {3}
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| Cell figure |
File:Regular polygon 3 annotated.svg {3}
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| Face figure |
File:Hexahedron.png {4,3}
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| Edge figure |
File:Schlegel wireframe 24-cell.png {3,4,3}
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| Vertex figure |
File:Demitesseractic tetra hc.png {3,3,4,3}
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| Dual |
24-cell honeycomb honeycomb
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| Coxeter group |
U5, [3,3,3,4,3]
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| Properties |
Regular
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In the geometry of hyperbolic 5-space, the 5-orthoplex honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,3,3,4,3}, it has three 5-orthoplexes around each cell. It is dual to the 24-cell honeycomb honeycomb.
Related honeycombs
Its vertex figure is the 16-cell honeycomb, {3,3,4,3}.
See also
References
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p. 212-213)
