Parities can occur in may types of cubes, yet parity doesn't actually have a definition in cubing. In this post, we will define parity as a situation in which the cube is unsolvable using the method you had been using for the solve. For example, without the parity alg for squan, the cube would be unsolvable. In this case, the parity alg is a different method which is introduced in order to solve the cube. But while most cubing parities occur due to swapped or rotated pieces, squans have defined orientations and permutations for all of its pieces, so this isn't possible. So why does it occur?
Squans are capable of shapeshifting/jumbling* which allows you to switch corners with edges. The first part of the solving process involves making the squan into a cube. However, when you make it a cube you can accidentally put edges in a position that would be unsolvable. It goes in a pattern. That's confusing, so here's an example: If two opposite edges are swapped on a 3x3, it is unsolvable. But if 4 opposite edges are swapped, well, we call that H-Perm. This translates to squan as when you are making it into a cube again, you have to place the edges. But it isn't possible to tell if your placing them in a solvable position. You might misplace two edges, which would result in a parity. But if you misplace four edges, it would be like you didn't misplace any edges at all. If the amount of misplaced edges is divisible by four, there won't be parity. If not, than there will be parity. There's two easy "If" statements. Maybe I'll cover those tomorrow...
Now, with this discovered, you might ask yourself "So, we can't tell how to prevent parity?" No, of course we can. This is America. With this much time on our hands we can do anything. When doing corner permutation (CP) you have to shapeshift the cube. By the time you reach CP, you can tell if you have parity. You can than recognize if you have it, and then modify your CP alg to accomadate this very easily, quickly eliminating parity. It is also technically possible to tell if you have parity as soon as you get cubeshape, but because whether or not you have parity can change as you solve (Like all parities), it's simply not worth it.
So in the end, Squan parity is an avoidable thing if you know how to deal with it. While this isn't as important to get fazt as other things, like cubeshape and EP, it is incredibly helpful as parity algs are long and take lots of time. So if you want to get fazt, better get started. Because weather you learn how to avoid parity or not, you have many algs ahead of you.
Of course I eat baby dwarves. How do you think I get this strong?
-GIR
*Again, neither of those have exact definitions and jumbling is only specified as shapeshifting that causes bandaging which is often voluntary. By voluntary I mean that it is possible to scramble the cube without jumbling. Jumbling also often switches pieces with other pieces that shouldn't go there. Example: An edge switching with a corner. This is exemplified in the curvy copter and helicopter cubes. But I digress. The point is, as squans meet all definitions for jumbling yet people call it shapeshifting, I don't actually know which one it is. In this post, I will simply call it shapeshifting.