Group theory studies how actions can be combined and reversed in patterns. Here, the actions are Nim additions — binary addition without carrying — and you prove that Nimbers (non-negative integers under this operation) form an Abelian group, a set where addition follows certain rules. When each Nimber maps to a point on a Simplex (a triangle or pyramid extended into more dimensions), the mapping turns out to be one-to-one: each Nimber matches exactly one point in multi-dimensional space. You build a 3D Simplex model using Zometool to see this in action and even use the Simplex graph to perform Nim addition visually.