Duoantifastegium

A duoantifastegium is a class of scaliform polytopes formed in a similar way to antiprisms, where the bases are two congruent prisms in opposite orientations, with the axis of one prism also orthogonal to the axis of the other. They can be seen as analogous to the more general duoantifastegiaprisms where one base is a digon. The simplest non-trivial duoantiwedge is the triangular duoantifastegium, in 5 dimensions. They are generally scaliform for any polygon {n/d} where n/d > 2, with the digonal case becoming a square disphenoid, which cannot be made scaliform due to requiring a height of 0.

In 5 dimensions, a duoantifastegium generally has 4 n-gonal antifastegiums and 2n square scalenes (seen as digonal antifastegiums) for facets, with a wedge pyramid shaped vertex figure..

The height of an n-gonal duoantifastegium is given by $$\sqrt{\frac{1-\frac{1}{1+\cos\frac{\pi}{n}}}{2}}$$.

Higher dimensional analogs do exist, but even the simplest of them, the tetrahedral duoantifastegium, would need to have a height of 0 to be scaliform and is equivalent to the demipenteract.