There are four different shapes of quadrilaterals here, but they have one thing in common: there are twelve of each of them. Add those 48 quads to the twelve regular heptagons, and that gives a total of 60 faces. I found this polyhedron while playing with the snub dodecahedron, using Stella 4d: Polyhedron Navigator, a program you can try for free right here.

In the image below, each of the four types of quadrilateral appears with its own color.