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. As such, they are also the convex hull of two orthogonal 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 and its conjugate, the pentagrammic double antiprismoid. The dual of a double antiprismoid is a double trapezohedroid. They are also a subset of 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.

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. This ensures that the sphenoids become tetragonal disphenoids.