The Truncated Cuboctahedron

The truncated cuboctahedron is created by truncating (cutting off) the cuboctahedron one third of the way into each side

26 total faces:
12 squares, 8 regular hexagons and 6 regular octagons

48 vertices:
1 square, 1 hexagon and 1 octagon

72 edges

Dihedral angles:  
135 degrees for the oct-sqr angle, 125 degrees,
16 minutes for the oct-hex angle and
144 degrees, 44 minutes for the hex-sqr angle