The gyrobifastigium is an octahedron with on 8 vertices, 14 edges, and 8 faces.
The equilateral gyrobifastigium is Johnson solid 
, consisting of two triangular
prisms joined at their bases with one rotated with respect to the other. It is
a space-filling polyhedron and stereohedron,
but not a plesiohedron.
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.
