Truncated Dodecahedron

The above Schlegel diagram of the truncated dodecahedron has 60 vertices and 90 edges. To create this structure, the vertices of the dodecahedron are "sliced" to create triangles. Then, the faces of the dodecahedron become decagons.

To tile this structure, we used two different tile types. The tiled structure is shown in the figure below

The two tile types are shown 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 dihedral angle between decagon and triangle faces is 142^o 37’ and it is 116o 34’ between two decagon faces. The angle between a triangle arm and a decagon arm is 144^o and the angle between two triangle arms is 60^o.