Truncated Cube

To create the truncated cube, the corners of a cube are "sliced off," creating equilateral triangles where the corners were and making the square faces of the cube into a regular octahedron. The final structure has 24 vertices and 36 edges. The above figure shows the tiling for the truncated cube in a Schlegel diagram using two bond edge types. The blue and orange represent a and its complement â, respectively, and the green and red represent b and its complement b̂, respectively.

Unlike the cube, however, the truncated cube has two different tile arm angles and two different dihedral angles. The angle between tile arms the form each triangle is 60^o and the angle between tile arms forming each octagon is 135^o. This is illustrated in the diagrams of the two tile types below.

The dihedral angle between two octagonal faces is 90^o and the angle between an octagonal face and a triangular face is 125^o 16'.