# Shen-Guan Shih and Min Shih

We are interested in discovery of forms and structures with simple elements that can be combined systematically to derive sophisticated forms. Symmetry is the common language in both art and mathematics. We consider the symmetry in geometry as well as the symmetry in process for the presented work.

The journey started from the challenge of dissecting a cube into interlocking parts of the same shape. This led to the discovery of an octocube called SL block. The presented work consists of 8640 interlocking SL blocks without using glue or any external support. There are 4 nested layers, each of which is composed of 9 interwoven frames. Each frame was built with SL blocks that are arranged into chain like configuration that may extend and turn in the 3 dimensional space. A mathematical representation based on non-commutative ring is devised to define interlocking compositions of SL blocks. Polynomials, equations and functions are used to represent composite structures formed by SL blocks.