Double antiprismoid

A double antiprismoid is an isogonal polytope formed from the alternation of a ditetragoltriate, a powertope formed by a polytope to the power of a ditetragon, if and and only if the base polytope is alternable. An n-gonal double antiprismoid is composed of two orthogonal rings of n n-gonal antiprisms each, with the rings aligned so that the edges belonging to the antiprisms' triangles on one ring are perpendicular to the other, creating tetragonal disphenoids. As such, they are also the convex hull of two duoantiprisms (made of similar but not congruent bases which are alternated polytopes) and are generally nonuniform. The simplest non-trivial double antiprismoid is the digonal double antiprismoid, while the only uniform double antiprismoids are the grand antiprism (n=5) and its conjugate, the pentagrammatic double antiprismoid (n=5/3). The dual of a double antiprismoid is a double trapezohedroid. They are also swirlchora based on an antiprism.

In four dimensions, the vertex figure of a double antiprismoid is a sphenocorona, except for the digonal double antiprismoid, which has a hexakis digonal-hexagonal gyrowedge vertex figure.

The n-gonal double antiprismoid could be generalized into an n-m double antiprismoid with rings of n- and m-gonal antiprisms respectively, with two vertex types.

Special cases
In four dimensions, an n-gonal double antiprismoid can have the least possible edge length difference if the ratio of the n-gons is equal to 1:(1+cos(π/n)+$\sqrt{(1+cos(π/n))^2-4cos(2π/n)}$)/2.