# Mathematical ImageryMathematicians and artists create strong, stunning, works in all media and explore the visualization of mathematics

# Notices of the American Mathematical Society: Cover Art

*Notices of the AMS*, the Society's member journal of record, has had some stunning covers over the years. Here is just a sampling.

"Kissing in Motion" shows the motion of the "shadows" of kissing spheres in a deformation pointed out by J.H. Conway and N.J.A. Sloane, following an observation of H.S.M. Coxeter. The sequence is left-right, right-left, left-right (sometimes called boustrophedon). The image accompanies "Kissing Numbers, Sphere Packings, and Some Unexpected Proofs," by Florian Pfender and Günter M. Ziegler (*Notices of the AMS*, September 2004, p. 873). - Bill Casselman

People have long been fascinated with repeated patterns that display a rich collection of symmetries. The discovery of hyperbolic geometries in the nineteenth century revealed a far greater wealth of patterns, some popularized by Dutch artist M. C. Escher in his Circle Limit series of works. This cover illustration portrays a pattern which is symmetric under a group generated by two Möbius transformations. These are not distance-preserving, but they do preserve angles between curves and they map circles to circles. The image accompanies "Double Cusp Group," by David J. Wright (*Notices of the AMS*, December 2004, p. 1322). - Bill Casselman

This image illustrates two types of infinite Coxeter groups and algorithms involved in computation within those groups: one which generates elements of the group one by one, the "Shortlex automaton," and others, more conjectural, which seem to describe the Kazhdan-Lusztig cells of an arbitrary Coxeter group. The illustration is described in detail and was created to accompany the article "Cells in Coxeter Groups," by Paul E. Gunnells (*Notices of the AMS*, May 2006, p. 528). The explicit finite state machines required to draw the Kazhdan-Lusztig cells were supplied by Gunnells. - Bill Casselman

This image exhibits fanciful renderings of the dyadic icosahedra discussed in the article "The p-adic Icosahedron," by Gunther Cornelissen and Fumiharu Kato (*Notices of the AMS*, August 2005, p. 720). - Bill Casselman