"The gyroelongated triangular bipyramid can be made with equilateral triangles"

Question

According to Wikipedia article Gyroelongated bipyramid

The gyroelongated triangular bipyramid can be made with equilateral triangles

I can only imagine that this would result in a cube, could you please explain otherwise?

Answer 1

The image in Wikipedia's table actually shows this configuration.

If you collapse each set of coplanar sides you get something with 6 quadrilateral faces that fit together like a cube, but each face is a rhombus with corner angles 60-120-60-120, rather than the cube's 90-90-90-90.

You can think of it as a cube that is stretched along one of the long (inner) diagonals.

Answer 2

The triangular bipyramid you're elongating is an octahedron. The image in your link shows that when you elongate it some of the new faces are coplanar with the old ones. There are six faces, but they are not squares. @HenningMalcom 's answer here describes those faces. This answer adds the fact that what you started with was an octahedron.