 8-simplex   
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 Heptellated 8-simplex
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 Heptihexipentisteriruncicantitruncated 8-simplex (Omnitruncated 8-simplex)
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| Orthogonal projections in A8 Coxeter plane (A7 for omnitruncation) | ||
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In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex.
There are 35 unique heptellations for the 8-simplex, including all permutations of truncations, cantellations, runcinations, sterications, pentellations, and hexications. The simplest heptellated 8-simplex is also called an expanded 8-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 8-simplex. The highest form, the heptihexipentisteriruncicantitruncated 8-simplex is more simply called a omnitruncated 8-simplex with all of the nodes ringed.