The Rubik’s Cube comes with 6 colors, one on each side. The task is straightforward. Restore a scrambled cube by twisting the layers to its solved state in which each side is a single color. There are variations of the 3x3x3 puzzle that add extra challenges.
The Nativity Cube page shows a solution of a picture cube. Picture cubes are cubes with pictures on each face instead of solid colors. This increases the challenge in two ways. It is usually more difficult to determine which pieces go together, and the orientation of the center pieces is important.
Sudoku Cubes are cubes with a number on each sticker. When solved the numbers 1 through 9 appear on each face of the cube. I worked out a solution based on how the numbers on a given piece are situated. Like with the picture cube, the centers must be twisted correctly for it to look right when solved. I have not memorized the arrangements of the numbers, nor do I refer to the pictures I took before scrambling the cube, so I have to think about the sudoku aspect when I solve it somewhat.
Fisher’s Cubes come in two types: single color and six color. The six color cube has one color for each side just like a normal Rubik’s, although the colors are a bit different. The single color cubes come in either silver or gold. Now what could be challenging about a twisty cube puzzle that has the same color on all 6 sides? Two of the sides have square center pieces. The other four sides have rectangular center pieces. Holding the cube so the sides with square centers are on top and bottom, when you turn a horizontal layer 90˚ the puzzle maintains its cube shape. But when you turn a vertical layer 90˚ it is no longer a cube. After enough twisting and turning, it is very irregular indeed. But they can still be solved using methods that work with Rubik’s Cubes. But it isn’t trivial, by any means. On a Rubik’s Cube each center has 1 color. Each edge has 2 colors. Each corner has 3 colors. On a Fisher’s Cube two of the centers correspond to Rubik’s Cube centers and have 1 color, but the other 4 centers of the Fisher’s Cube correspond to Rubik’s Cube edges, yet on the Fisher’s Cube they have only 1 color. I could go on but it just gets more convoluted.
The Meffert’s Master Pyramorphinx is a tetrahedron shaped puzzle. A triangular pyramid. It is pillowed. That is the corners and edges are rounded, not sharp, and the faces are rounded, not flat. Take it apart and you will find a core that looks like a normal cube core. On the page I describe some similarities and differences between a Master Pyramorphinx and a Rubik’s Cube, and I present one strategy for solving it. If you can solve a Rubik’s Cube you should be able to almost solve the Master Pyramorphinx. If you can solve a picture cube, you know everything you need to know to solve the Master Pyramorphinx. The challenge is in applying what you know to something that looks so utterly different.
The Octagonal Prism aka Space Shuttle is another puzzle that is a modification of the 3×3×3 cube. Another puzzle with some interesting challenges.
The Rhombic Dodecahedron is yet another shape modification of the 3×3×3 cube. The page tells some similarities and differences and a strategy for solving it.
The Octahedral 3x3x3 is another shape modification of the 3x3x3 cube. Let’s sum up: Rubik’s is a 6-sided 3x3x3 cube; Fisher’s is a shape-shifting cube; Master Pyramorphinx is a 4-sided 3x3x3; Octahedral is an 8-sided 3x3x3; Rhombic Dodecahedron is a 12-sided 3x3x3.
The Megaminx is not a shape modification of the 3×3×3 cube. But it is a 3×3×3 cube-like puzzle in the way that you can solve it. White edges; F2L; middle section using white edge and F2L moves; top edges; top corners.