The Art and Mathematics of Self-interlocking `SL` Blocks

Shen-Guan Shih

Department of Architecture

National Taiwan University of Science and Technology

sgshih@mail.ntust.edu.tw

    `SL` block is an octocube that may interlock with other `SL` blocks to form infinite variations of stable structures. The property of self-interlocking makes `SL` block expressive to explore the beauty of symmetry, which has been regarded as an essence of art and mathematics by many. This paper describes a mathematical representation that maps polynomial expressions to compositions of `SL` blocks. The use of polynomials, functions and hierarchical definitions simplifies the creation, communication and manipulation of complex structures by making abstractions over symmetrical parts and relationships. The discovery of `SL` block and its mathematical representation lead the way towards the development of an expressive language of forms and structures which is at the same time, rich and compact, free and disciplined.

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