The great icosidodecahedron is one of the uniform polyhedra, which I do not know well. I stumbled across it while creating facetings of the (lesser) icosidodecahedron. This solid has two face-types, there are red pentagrams and yellow equilateral triangles, as seen in the next two pictures.

The dual of this solid is the great rhombic triacontahedron. Its faces are thirty interpenetrating rhombi.

I used Stella 4d to create these images. You may try this program for free at http://www.software3d.com/Stella.php.