I am trying to solve a computer modeling problem that involves decomposing a random geometry into a set of primitives and am looking for the name of a branch of mathematics that helps me do so.
As a simple two-dimensional example, a regular hexagon can be decomposed into six identical triangles. In three dimensions, a Rubik's cube can be decomposed into its 3 x 3 x 3 = 27 smaller cubes. However, there will never be a unique solution--for example, the same cube can be decomposed into a set of geometries that are not self similar [e.g. (2 x 2 x 2) + (3 x 3 x 1) + (3 x 2 x 1) + (2 x 2 x 1)].
I assume that there must be some branch of mathematics that involves decomposing an N-dimensional object into a set of N-dimensional smaller objects--can somebody tell me what this branch is called?
I hope this is a bit clearer (?)