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.

Generally, their vertex figures alternate depending on whether the base polytope has central inversion symmetry. For example, the triangular double antiprismoid and the grand antiprism have sphenocorona vertex figures, while the square double antiprismoid and hexagonal double antiprismoid have topologically different vertex figures; the former has 2 trapezoids and 14 triangles with 8 meeting at an 8-valence vertex, while the latter has 2 trapezoids and 18 triangles with 10 meeting at a 10-valence vertex.