# Duoantiprism

A **duoantiprism** is an isogonal polytope formed from the alternation of a duoprism formed as the Cartesian product of two polytopes, if and and only if both base polytopes are alternable, and are generally nonuniform. The simplest non-trivial duoantiprism is the hexadecachoron (considered as a digonal duoantiprism), while the only uniform duoantiprisms are the hexadecachoron (and any demihypercube) and the great duoantiprism (pentagonal-pentagrammic crossed duoantiprism). The dual of a duoantiprism is a duoantitegum. They are also a special class of the duoprismatic swirlprisms, having only two polygonal rotations for each ring.

4D duoantiprisms generally have 2 orthogonal rings of antiprismatic cells, connected by digonal disphenoids. If the two base polygons are identical the disphenoids become tetragonal disphenoids and the two rings of antiprisms become identical. They generally have vertex figures that are variants of the Johnson solid gyrobifastigium. If one of the base polygons is a digon, the digonal antiprisms are tetragonal disphenoids, and the vertex figure becomes a variant of the augmented triangular prism instead.

Duoantiprisms exist in higher dimensions as well. They generally have lower duoantiprisms, or simple antiprisms, as cells along with various lower-symmetry simplices.

## Special cases[edit | edit source]

In four dimensions, a duoantiprism can have the least possible edge length difference if both base polygons have the same edge length. This ensures that the digonal disphenoids become tetragonal disphenoids.

## External links[edit | edit source]

- Klitzing, Richard. "n,m-dap".

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