Just as there are semiregular polyhedra in 3D in contrast to regular polyhedra, there are semiregular polychors in 4D in contrast to regular polychors.
There are 13 semiregular polyhedra, known as Archimedean solids. These are composed of two or more types of regular polygons. Moreover, there are Archimedean prisms (prisms with regular polygonal top and bottom faces and square side faces) and Archimedean antiprisms (regular polygonal top and bottom faces and equilateral triangular side faces) - which are composed of two or more types of regular polygons as well.
There are 58 four-dimensional semiregular shapes, which are composed of two or more types of regular polyhedra, semiregular polyhedra, Archimedean prisms, or Archimedean antiprisms. Of the 58 types, 17 are hyperprisms, whose "side cells" are cubes and whose "top" and "bottom" faces are regular or semiregular polyhedra other than cubes. The other 41 types of semiregular polytopes include 8 types derived from Pen, 12 types derived from Tes or Hex, 6 types derived from Ico, 13 types derived from Hi or Ex, and 2 types of twisted polytopes.
Note: In Japan, the term semiregular polychora refers to the 4D analogs of the Archimedean solids. However, it seems that, for English speakers, a semiregular polytope is "an isogonal polytope that only contains regular facets." With this definition, there are only 3 convex semiregular polychora, while there are more nonconvex ones.
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