Pentagrammic-order 600-cell honeycomb

Pentagrammic-order 600-cell honeycomb
(No image)
TypeHyperbolic regular honeycomb
Schläfli symbol{3,3,5,5/2}
Coxeter diagram
4-faces {3,3,5}
Cells {3,3}
Faces {3}
Face figure {5/2}
Edge figure {5,5/2}
Vertex figure {3,5,5/2}
DualSmall stellated 120-cell honeycomb
Coxeter groupH4, [5,3,3,3]
PropertiesRegular

In the geometry of hyperbolic 4-space, the pentagrammic-order 600-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,3,5,5/2}, it has five 600-cells around each face in a pentagrammic arrangement. It is dual to the small stellated 120-cell honeycomb. It can be considered the higher-dimensional analogue of the 4-dimensional icosahedral 120-cell and the 3-dimensional great dodecahedron. It is related to the order-5 icosahedral 120-cell honeycomb and great 120-cell honeycomb: the icosahedral 120-cells and great 120-cells in each honeycomb are replaced by the 600-cells that are their convex hulls, thus forming the pentagrammic-order 600-cell honeycomb.

This honeycomb can also be constructed by taking the order-5 5-cell honeycomb and replacing clusters of 600 5-cells meeting at a vertex with 600-cells. Each 5-cell belongs to five such clusters, and thus the pentagrammic-order 600-cell honeycomb has density 5.

See also

References

This article is issued from Wikipedia - version of the 2/19/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.