This is the truncated cube, which is one of the Archimedean solids.
To make a faceted version of this solid, one must connect at least some of the vertices in different ways. Doing that creates new faces.
This faceted version of the truncated cube includes eight blue equilateral triangles, eight larger, yellow equilateral triangles, and eight irregular, red hexagons. It’s easy to spot the yellow and blue triangles, but seeing the red hexagons is harder. In the final picture here, I have hidden all faces except for three of the hexagons, so that their positions can be more easily seen.
I made all three of these images using Robert Webb’s program called Stella 4d: Polyhedron Navigator. It is available for purchase, or as a free trial download, at http://www.software3d.com/Stella.php.