I’ve been having a lot of fun with infinity mirrors, and recently built an infinity octahedron from laser-cut partially mirrored acrylic. An octahedron makes a particularly nice base for an infinity polyhedron because you can run a single continuous path of LED strips that covers all edges without having to double the strip back on itself. The mirrored sides of this particular build are held together with acrylic connectors at each vertex.
The design files for this build and an overview of the build process are up on my GitHub at: https://github.com/geekmomprojects/InfinityOctahedron
