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 by the two opposite points, as in the case of Prince Rupert's problem. If the aspect ratio is not constrained, the rectangle with the largest area that fits within a cube is the one that has two opposite edges of the cube as two of its sides, and two face diagonals as the other two sides. Alternatively, one may ask for the largest formula_4-dimensional hypercube that may be drawn within an formula_5-dimensional unit hypercube. The answer is always an algebraic number. For instance, the problem for formula_6 asks for the largest cube within a four-dimensional hypercube. After Martin Gardner posed