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
Prince Rupert's cube the hole through which a cube larger than the original one (up to side length formula_2) may pass. The parts of the unit cube that remain, after emptying this hole, form two triangular prisms and two irregular tetrahedra, connected by thin bridges at the four vertices of the square. Each prism has as its six vertices two adjacent vertices of the cube, and four points along the edges of the cube at distance 1/4 from these cube vertices. Each tetrahedron has as its four vertices one vertex of the cube, two points at distance 3/4 from it on two of