In geometry, an E₉ honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. ${\displaystyle {\bar {T}}_{9}}$, also (E₁₀) is a paracompact hyperbolic group, so either facets or vertex figures will not be bounded.

E₁₀ is last of the series of Coxeter groups with a bifurcated Coxeter-Dynkin diagram of lengths 6,2,1. There are 1023 unique E₁₀ honeycombs by all combinations of its Coxeter-Dynkin diagram. There are no regular honeycombs in the family since its Coxeter diagram is a nonlinear graph, but there are three simplest ones, with a single ring at the end of its 3 branches: 6₂₁, 2₆₁, 1₆₂.

The 6₂₁ honeycomb is constructed from alternating 9-simplex and 9-orthoplex facets within the symmetry of the E₁₀ Coxeter group.

This honeycomb is highly regular in the sense that its symmetry group (the affine E₉ Weyl group) acts transitively on the k-faces for k ≤ 7. All of the k-faces for k ≤ 8 are simplices.

This honeycomb is last in the series of k₂₁ polytopes, enumerated by Thorold Gosset in 1900, listing polytopes and honeycombs constructed entirely of regular facets, although his list ended with the 8-dimensional the Euclidean honeycomb, 5₂₁.

It is created by a Wythoff construction upon a set of 10 hyperplane mirrors in 9-dimensional hyperbolic space.

The facet information can be extracted from its Coxeter-Dynkin diagram.

Removing the node on the end of the 2-length branch leaves the 9-orthoplex, 6₁₁.