laminated

Laminated puzzle simulator.

What is it

Consider a set $R$ of objects called rays and a group $G$ that acts transitively on the set of rays. We can define an equivalence relation on rays where $r \sim r'$ whenever $G_r = G_{r'}$, where $G_r$ is the stabilizer of $r$ in $G$. The equivalence classes are then called axes. Then, given an axis, a grip along that axis assigns a certain 'distance' along each ray in the axis. A group element $g$ applies to a grip to produce a new grip by transforming each axis in the corresponding ray. We can then create a finite set of grips closed under the group action, and construct the set of all pieces, where a piece has one grip along each axis. This is a laminated puzzle. The puzzle can be twisted by a group element $g$ and a grip whose axis is stabilized by $g$ by applying $g$ to each piece that contains that grip.

With this construction, it can be seen that laminated puzzles contain a subset of the pieces of complex puzzles. However, laminated puzzles are closer to real puzzles in that they have parallel layers that do not intersect. If the set of rays exists on a sphere, the laminated puzzle is the puzzle that contains all holding point pieces.

Features

laminated supports laminated face-turning cubes, octahedra, dodecahedra, and rhombic dodecahedra.

Running

Clone this repository and run cargo run --release in the directory.