Pocket Cube Rubik's cube, simply by treating it as a 3x3x3 with solved (invisible) centers and edges. More advanced methods combine multiple steps and require more algorithms. These algorithms designed for solving a 2x2x2 cube are often significantly shorter and faster than the algorithms one would use for solving a 3x3x3 cube. The Ortega method, also called the Varasano method, is an intermediate method. First a face is built (but the pieces may be permuted incorrectly), then the last layer is oriented (OLL) and lastly both layers are permuted (PBL). The Ortega method requires a total of 12 algorithms. The CLL method
Prince Rupert's cube for the largest square that lies within a unit cube. More generally, show how to find the largest rectangle of a given aspect ratio that lies within a unit cube. As they show, the optimal rectangle must always pass through the center of the cube, with its vertices on edges of the cube. Based on this, they show, depending on the desired aspect ratio, that the optimal rectangle must either lie on a plane that cuts diagonally through four corners of the cube, or it must be formed by an isosceles right triangle on one corner of the cube and