6 square faces
8 vertices
6 octagonal faces,
8 triangular faces
|
6 square faces 8 vertices |
6 octagonal faces, 8 triangular faces |
To cut off the corners of the cube, we move in the same distance from each corner along the edges. The distance we move is less than half of the side length, because it is impossible to move in more. (If we move in exactly half way, the result is the cuboctahedron)
This process shortens the side lengths of the edges in the original cube by the same amount. Notice that it also doubles the number of edges -- changing the purple square faces of the cube (left) into purple octagonal faces in the truncated cube (right).
In the cube, three faces meet at every vertex. Cutting off the original vertices, then, leaves a triangular shape behind, which is filled in by the green triangles.