Ditetragoltriate

A ditetragoltriate is a powertope formed by a polytope to the power of a ditetragon, which is equivalent to the convex hull of two duoprisms (made of similar but not congruent bases, but in the same orientation, and with the larger base on different axes in each case). Any n-dimensional isogonal base polytope has an isogonal ditetragoltriate in 2n dimensions.

In four dimensions, n-gonal ditetragoltriates generally consist of 2 rings of prisms with lacing edges longer than those of the bases of the prism, connected by a layer of rectangular trapezoprisms. Their vertex figures are generally notches. They are also swirlchora and the first member based on the n-gonal prisms. The simplest non-trivial ditetragoltriate is the triangular ditetragoltriate. Variants based on semi-uniform polygons such as the rectangle also exist that remain fully isogonal. Ditetragoltriates also exist in higher even dimensions.

The dual of a ditetragoltriate is a tetrambitriate. If the base is alternable, then it can be alternated into a double antiprismoid, with simplexes filling the gaps left behind by the deleted vertices.

Special cases

In four dimensions, an n-gonal ditetragoltriate can have the least possible edge length difference (both via the absolute-value method and the ratio method) if the ratio of the n-gons is equal to 1:1+√2sin(π/n). This ensures that the isosceles trapezoids have three equal edges.