Cyclotruncated 5-simplex honeycomb explained

bgcolor=#e7dcc3 colspan=2Cyclotruncated 5-simplex honeycomb
bgcolor=#ffffff align=center colspan=2(No image)
TypeUniform honeycomb
FamilyCyclotruncated simplectic honeycomb
Schläfli symbolt0,1
Coxeter diagram or
5-face types
4-face types
Cell types
Face types
Vertex figure
Elongated 5-cell antiprism
Coxeter groups

{\tilde{A}}5

×22, 3[6]
Propertiesvertex-transitive
In five-dimensional Euclidean geometry, the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed of 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets in a ratio of 1:1:1.

Structure

Its vertex figure is an elongated 5-cell antiprism, two parallel 5-cells in dual configurations, connected by 10 tetrahedral pyramids (elongated 5-cells) from the cell of one side to a point on the other. The vertex figure has 8 vertices and 12 5-cells.

It can be constructed as six sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 5-cell honeycomb divisions on each hyperplane.

See also

Regular and uniform honeycombs in 5-space:

References