However, when the equilateral gyrobifastigium is "squashed" so that it has isosceles right triangular faces and quadrilateral faces consisting of rectangles
with sides in the ratio of , it becomes a plesiohedron.

These variants are illustrated above, together with the canonical version. They are implemented in the Wolfram
Language as PolyhedronData["EquilateralGyrobifastigium"],
PolyhedronData[PlesiohedralGyrobifastigium"],
and PolyhedronData["CanonicalGyrobifastigium"],
respectively.