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Related polytopes and honeycombs

The pentachoron (5-cell) is the simplest of 9 uniform polychora constructed from the Coxeter group.

It is in the {p,3,3} sequence of regular polychora with a 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.

It is one of three {3,3,p} regular 4-polytopes 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.

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