Double gyroantiprismoid

A double gyroantiprismoid is an isogonal polytope formed in a similar way to the double antiprismoids, but with two antialigned rings. An n-gonal double gyroantiprismoid is composed of two orthogonal rings of n n-gonal antiprisms each, with the rings aligned so that the edges belonging to the n-gons on one ring are perpendicular to the other, creating tetragonal disphenoids, with rhombic disphenoids and sphenoid filling the remaining gaps. Like the double antiprismoids, they are also the convex hull of two orthogonal duoantiprisms (made of similar but not congruent bases which are alternated polytopes) and are nonuniform. The simplest non-trivial double gyroantiprismoid is the triangular double gyroantiprismoid, because the digonal double gyroantiprismoid is the octagonal duotegum. The dual of a double gyroantiprismoid is a double gyroantitegmoid. They have the same symmetry as the duoantiprisms.

In four dimensions, the vertex figure of a double antiprismoid is an octakis digonal-octagonal gyrowedge, which generally has 2 trapezoidal and 14 triangular faces. The digonal double antiprismoid has an octagonal tegum vertex figure as the trapezoidal faces collapse back into triangles.

Special cases

In four dimensions, an n-gonal double gyroantiprismoid can have the least possible edge length difference if the ratio of the n-gons is equal to 1:1+√2sin(π/n) (for n less than 7) or 1:tan(π/n)+sec(π/n) (for n equal or greater than 7).