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
Halved cube graph in the original graph. For instance, the halved cube graph of order four may be formed from an ordinary three-dimensional cube by keeping the cube edges and adding edges connecting pairs of vertices that are on opposite corners of the same square face. The halved cube graph formula_2 of order 3 is the complete graph "K", the graph of the tetrahedron. The halved cube graph formula_3 of order 4 is "K", the graph of the four-dimensional regular polytope, the 16-cell. The halved cube graph formula_4 of order five is sometimes known as the Clebsch graph, and is the complement of