Bidiakis cube theorem, it is a 3-vertex-connected simple planar graph. The Bidiakis cube is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 8, the group of symmetries of a square, including both rotations and reflections. The characteristic polynomial of the Bidiakis cube is formula_1. 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
Cube faces and eight triangular ones. In particular we can get regular octagons (truncated cube). The rhombicuboctahedron is obtained by cutting off both corners and edges to the correct amount. A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes. If two opposite corners of a cube are truncated at the depth of the three vertices directly connected to them, an irregular octahedron is obtained.