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
Prince Rupert's cube the adjacent edges, and one point at distance 3/16 from the cube vertex along the third adjacent edge. Prince Rupert's cube is named after Prince Rupert of the Rhine. According to a story recounted in 1693 by English mathematician John Wallis, Prince Rupert wagered that a hole could be cut through a cube, large enough to let another cube of the same size pass through it. Wallis showed that in fact such a hole was possible (with some errors that were not corrected until much later), and Prince Rupert won his wager. Wallis assumed that the hole would be parallel