Alternated prism

The second definition refers to an alternated prism where the base is alternatable, such as the snub cubic antiprism, derived from the great rhombicuboctahedral prism, and the hexadecachoron (tetrahedral antiprism), derived from the tesseract (cubic prism). Unlike the first definition, 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, antiprisms in this sense, 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 antiprism (under the second definition) is a wedge derived from a simplex two dimensions lower than the antiprism 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.