Omnitruncated 5-cell

In four dimensional geometry, the omnitruncated 5-cell is a uniform polychoron.

Alternative names

* Omnitruncated 5-cell
* Omnitruncated pentachoron
* Omnitruncated 4-simplex
* Great prismatodecachoron
* Gippid (Jonathan Bowers: for great prismatodecachoron)

Just as the truncated octahedron is the permutohedron of order 4, the omnitruncated 5-cell is the permutohedron of order 5. [ [http://www.math.ubc.ca/~holroyd/cayley/s5.html The permutahedron of order 5] ] The omnitruncated 5-cell is a zonotope, the Minkowski sum of five line segments parallel to the five lines through the origin and the five vertices of the 5-cell.

Tessellations

The omnitruncated 5-cell can tessellate 4-dimensional space by itself with 3 hypercells around each face. It has Coxeter-Dynkin diagram of s, this honeycomb has only one such construction.

=

ee also

* Uniform polychoron

External links

* [http://members.aol.com/Polycell/section1.html Convex uniform polychora based on the pentachoron (5-cell)] , George Olshevsky (9)