Bidiakis cube Bidiakis cube In the mathematical field of graph theory, the Bidiakis cube is a 3-regular graph with 12 vertices and 18 edges. The Bidiakis cube is a cubic Hamiltonian graph and can be defined by the LCF notation [-6,4,-4]. The Bidiakis cube can also be constructed from a cube by adding edges across the top and bottom faces which connect the centres of opposite sides of the faces. The two additional edges need to be perpendicular to each other. With this construction, the Bidiakis cube is a polyhedral graph, and can be realized as a convex polyhedron. Therefore, by Steinitz's
Truncated cube The truncated triangular trapezohedron is another polyhedron which can be formed from cube edge truncation. The "truncated cube", is second in a sequence of truncated hypercubes: In the mathematical field of graph theory, a truncated cubical graph is the graph of vertices and edges of the "truncated cube", one of the Archimedean solids. It has 24 vertices and 36 edges, and is a cubic Archimedean graph. Truncated cube In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices. If the truncated cube has