Pentagonal ditetragoltriate

The pentagonal ditetragoltriate or pedet is a convex isogonal polychoron and the third member of the ditetragoltriate family. It consists of 10 pentagonal prisms and 25 rectangular trapezoprisms. 2 pentagonal prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal pentagonal prismatic swirlchora.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform pentagonal duoprisms, one with a larger xy pentagon and the other with a larger zw pentagon.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{5-\sqrt5}}{2}$$ ≈ 1:1.83125. This value is also the ratio between the two sides of the two semi-uniform duoprisms.

The grand antiprism can be thought of as the convex hull of two inversely oriented pentagonal ditetragoltriates, with the pentagons having a ratio of 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.