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
V-Cube 7 for a 3×3×3 cube. Because the permutations of the corners, central edges and fixed centers have the same parity restrictions as the 3×3×3 cube, once reduction is complete the parity errors seen on the 4×4×4 and 6×6×6 cannot occur on the 7×7×7. Another strategy is to solve the edges of the cube first. The corners can be placed just as they are in any previous order of cube puzzle, and the centers are manipulated with an algorithm similar to the one used in the 4×4×4 cube. The world record time for a single solve is 1 minute, 47.89 seconds, set