These images illustrate a variety of kinds of symmetrical figures; most were produced for "The Symmetries of Things," written with John H. Conway and Heidi Burgiel (A.K. Peters, 2008), using a variety of proprietary software tools.I have been interested in geometry, pattern, and mathematical illustration of one form or another since I was a child. Abstraction is the basis of the power of mathematics, but too often we forget that mathematics is also a descriptive language, with meaning anchored in intuitive experience of the world around us. How many students emerge from, say, an undergraduate linear algebra course for math majors, knowing full well proofs of the existence and characterization of eigenspaces and eigenvalues, having no simple, clear idea of what such objects might look like?

Though I am as seduced by abstraction as any research mathematician, I am drawn to mathematics I can see and touch; mathematical illustration, carried out in a graphically rigorous manner, is a natural extension of my work as a mathematician--and indeed may be more fundamental to me.

— *Chaim Goodman-Strauss, University of Arkansas*

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