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
Compound of 5-cube and 5-orthoplex different edges. Compound of 5-cube and 5-orthoplex In 5-dimensional geometry, the 5-cube 5-orthoplex compound is a polytope compound composed of a regular 5-cube and dual regular 5-orthoplex. A "compound polytope" is a figure that is composed of several polytopes sharing a common center. The outer vertices of a compound can be connected to form a convex polytope called the convex hull. The compound is a facetting of the convex hull. In 5-polytope compounds constructed as dual pairs, the hypercells and vertices swap positions and cells and edges swap positions. Because of this the number of hypercells and vertices are equal,