To make this polyhedron using Stella 4d (available here), I began with the dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and then stellated it thirteen times. 

This stellated polyhedron has pyritohedral symmetry, but this is easier to see in its convex hull:

The eight blue triangles in this convex hull are equilateral, while the twelve yellow ones are golden isosceles triangles.