This polyhedron has tetrahedral symmetry, and eight faces. Four of them are equilateral triangles, while the other four are 6/2-gons. I made it by modification of the truncated tetrahedron, using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.

This polyhedron’s faces are six rhombi, and twelve kites. I came across it by modifying the truncated tetrahedron, using Stella 4d: Polyhedron Navigator. You can try this software for free at this website.