Alternated prism

An alternated prism is derived as an alternated prism where the base is alternable. Examples include the snub cubic antiprism, derived from the great rhombicuboctahedral prism, and the hexadecachoron (tetrahedral antiprism), derived from the tesseract (cubic prism). Unlike the antiprisms formed from dual bases, it only includes bases that are congruent and does not necessarily imply self-duality.

Duoantiprisms, following from the second definition, are alternations of duoprisms. The grand antiprism is confusingly named as such, although it is actually an alternated decagonal ditetragoltriate.

Unlike prisms, alternated prisms, as for arbitrary alternations, in four dimensions or greater generally have no uniform realization, because there are too many edge lengths to be rescaled to equal length. Exceptions do exist in any dimension, as the demihypercubes, derived from hypercubes, can always be made uniform.

The vertex figure of an alternated prism is a wedge derived from a simplex two dimensions lower than the alternated prism and the base's vertex figure. For example, the vertex figure of a demipenteract (hexadecachoric antiprism) is a rectified pentachoron, which is a wedge of a tetrahedron and an octahedron.