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
Klee–Minty cube algorithms and also for interior-point algorithms. The Klee–Minty cube was originally specified with a parameterized system of linear inequalities, with the dimension as the parameter. When the dimension is two, the "cube" is a squashed square. When the dimension is three, the "cube" is a squashed cube. Illustrations of the "cube" have appeared besides algebraic descriptions. The Klee–Minty polytope is given by This has "D" variables, "D" constraints other than the "D" non-negativity constraints, and 2 vertices, just as a "D"-dimensional hypercube does. If the objective function to be maximized is and if the initial vertex for the simplex algorithm