Pentagonal double antitegmoid

The pentagonal double trapezohedroid is a convex isochoric polychoron and member of the double trapezohedroid family with 100 order-5 truncated bi-apiculated tetrahedra as cells. It can be obtained as the dual of the uniform grand antiprism. It is the first in an infinite family of isochoric pentagonal trapezohedral swirlchora.

Being the dual of the grand antiprism, this shape is sometimes called the grand trapezohedron, in analogy to how trapezohedra are the duals of antiprisms. Despite this name, this shape is neither a stellation nor a trapezohedron in any common sense of the word.

The cells of this polychoron can be constructed by augmenting tall pyramids onto two of the faces of a regular dodecahedron. As such they each have 4 identical geometrically regular pentagonal faces, with 2 isosceles trapezoids and 4 kites as well.

The ratio between the longest and shortest edges is $$1:\frac{3+\sqrt5}{4}\approx 1:2.61804$$.