Great Rhombicuboctahedron

The great rhombicuboctahedron has 48 vertices and 72 edges. The tiled Schlegel diagram is shown in the figure above. We were able to tile this structure using three tile types (as shown in the figures below).

The orange lines represent the bond edge type a and blue lines represent the complement â; the red lines represent the bond edge type b and the green lines represent its complement b-hat; the yellow lines represent the bond edge type c and the purple lines represent its complement ĉ. The arms that make the square faces have 90^o, the arms that make up the hexagons have 120^o between them, and the arms of the octagon have 144^o between them.