Great Rhombicosidodecahedron

The great rhombicosidodecahedron has 120 vertices and 180 edges. When tiling this structure, we were able to use three different tile types, which are depicted in the figure below.

The blue lines represent the bond edge type a and the orange lines represent its complement â; the green lines represent the bond edge type b and the red lines represent its complement b-hat; the purple lines represent the bond edge type c and the yellow lines represent its complement ĉ. The dihedral angle between a decagon face and square face is 148^o 17', between a decagon face and hexagon face it is 142^o 37', and the angle between the hexagon face and square face is 159^o 6'. The angle between arms making the decagon faces is 144^o, the angle between arms making the hexagon faces is 120^o, and the angle between arms making square faces is 90^o.