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
Centered cube number Centered cube number A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with "i" points on the square faces of the "i"-th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has "n" + 1 points along each of its edges. The first few centered cube numbers are The centered cube number for a pattern with "n" concentric layers around the central point is given by the formula The same number