Somap

A 3d visualization of the SOMAP, the graph of the relationships between the solutions to the SOMA cube. This app is about the SOMA cube, not the Rubik's Cube. If you are not familiar with the SOMA cube, this app will probably be of no interest, but if you're curious read on. There are 240 unique solutions (counting reflections as the same) to the Soma Cube. With one exception (detailed below) given any one of the solutions it is possible to remove two or three of the pieces, change their orientation (separately or as a unit) and put them back to again form a cube but a different one of the solutions. This is called a connection or a relationship between those two cubes. The more interesting discovery is that there are structures to be found among these connections. There are many connections where two pieces are rotated together to get a second cube, then rotated again to get a third, and rotated again to get back to the first cube. Each of those three cubes then have another set of pieces that are in the same orientation in all three, and so doing the same transformation on each connects to a second set of three cubes that together forn another cycle of three connections. This goes on twice mmore so that the whole structure could be thought of as a cylinder. Most of the obvious structures have been given names for reference. You can toggle each one visible/hidden and also highlight a structure for easier recogniztion. You can toggle the visibility of the pair or triple connections. There are several connections that stretch across the map, you can hide them which can make it easier to see the structures. Each of the seven pieces is given a name and a color. William McKeeman used a color scheme based on the colors of the rainbow. John Conway used a different color scheme. This app lets you switch between the two. Each cube in the visualization is in the standard orientation (The 'T' shaped piece at the bottom front; it can be proved that this piece cannot be in any other orientation') There is one cube among the 240 that has no connections, no relationships to any other cube. This is called the Lazarus Cube, after the character in the Star Trek episode called "The Alternative Factor" who has to spend eternity with only his mirror image.   Currently this app is only a visualization tool, you can't interract with the cubes or connections in any way.