Semiregular polytope

E.L. Elte compiled a longer list in 1912 as The Semiregular Polytopes of the Hyperspaces which included a wider definition.

In three-dimensional space and below, the terms semiregular polytope and uniform polytope have identical meanings, because all uniform polygons must be regular.

However, since not all uniform polyhedra are regular, the number of semiregular polytopes in dimensions higher than three is much smaller than the number of uniform polytopes in the same number of dimensions.

These were all listed by Gosset, but a proof of the completeness of this list was not published until the work of Makarov (1988) for four dimensions, and Blind & Blind (1991) for higher dimensions.

Gosset honeycombs: Semiregular E-honeycomb: Gosset (1900) additionally allowed Euclidean honeycombs as facets of higher-dimensional Euclidean honeycombs, giving the following additional figures: There are also hyperbolic uniform honeycombs composed of only regular cells (Coxeter & Whitrow 1950), including:

The tetrahedral-octahedral honeycomb in Euclidean 3-space has alternating tetrahedral and octahedral cells.
The hyperbolic tetrahedral-octahedral honeycomb has tetrahedral and two types of octahedral cells.