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In geometry an omnitruncated simplectic honeycomb or omnitruncated n-simplex honeycomb is an n-dimensional uniform tessellation, based on the symmetry of the A ~ n {\displaystyle {\tilde {A}}_{n}} affine Coxeter group. Each is composed of omnitruncated simplex facets. The vertex figure for each is an irregular n-simplex.
The facets of an omnitruncated simplectic honeycomb are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers.
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