Editing 5-cell (section)

== Related polytopes and honeycombs ==
The pentachoron (5-cell) is the simplest of 9 [[Uniform polychoron|uniform polychora]] constructed from the [3,3,3] [[Coxeter group]].
{{Pentachoron family small}}

{{1 k2 polytopes}}

{{2 k1 polytopes}}

It is in the {p,3,3} sequence of [[regular polychora]] with a [[tetrahedron|tetrahedral]] [[vertex figure]]: the [[tesseract]] {4,3,3} and [[120-cell]] {5,3,3} of Euclidean 4-space, and the [[hexagonal tiling honeycomb]] {6,3,3} of hyperbolic space.
{{Tetrahedral vertex figure tessellations small}}

It is one of three {3,3,p} [[regular 4-polytope]]s with tetrahedral cells, along with the [[16-cell]] {3,3,4} and [[600-cell]] {3,3,5}. The [[order-6 tetrahedral honeycomb]] {3,3,6} of hyperbolic space also has tetrahedral cells.
{{Tetrahedral cell tessellations}}

It is self-dual like the [[24-cell]] {3,4,3}, having a [[palindromic]] {3,p,3} [[Schläfli symbol]].
{{Symmetric_tessellations}}

{{Symmetric2_tessellations}}