Meta-Rule/Composition

Symmetries as a collection of possibilities

According to Mathemaniac, symmetries can be thought of as mathematical operands that gets to be manipulated through some operations that preserves the properties of being symmetrical. These four most general properties are:

1. Closure: Symmetrical operations on symmetries always create symmetries
2. Associativity: Symmetries composition with symmetries are symmetries Associative
3. Identity: Doing nothing is a symmetrical operation
4. Inverse Exists: Symmetrical operations can be undone, and returns to the original symmetry.

Meta-Rule