# Teruhisa Sugimoto

For the longest time, tessellation (tiling), covering, and packing have fascinated me, especially tessellations of convex pentagons, with which I have had a relationship for roughly half of my life. While much of my time has been spent doing mathematical exploration, I have always carried with me a sense of artistic curiosity, and, in recent years, I have spent a lot of time on artistic activities.

In 1995, Marjorie Rice discovered an interesting tessellation by using convex pentagons. The tessellation decorates the floor of lobby in the Mathematical Association of America headquarters. The convex pentagon which Rice used in the discovery belongs to both Type 1 and Type 5 of the known types for convex pentagonal tiles. I found novel properties of the convex pentagon. This artwork is a tessellation of that convex pentagon, using the properties I discovered. In this tessellation, according to a certain rule, the anterior pentagons have three kinds of warm colors, and the posterior pentagons have three kinds of cool colors. This convex pentagon tessellation is related to heptiamond tessellation.

An interesting convex pentagon tessellation, which Marjorie Rice
discovered in 1995, is formed by a convex pentagonal tile
belonging to Type 1 and Type 5. Hereafter, the tessellation
discovered by Marjorie Rice is called a Rice1995-tiling. It seems
at first that the Type 5 tessellation and the Rice1995
tessellation, each formed by using the same convex pentagonal
tile, are different patterns. In fact, there exists a property
such that the Type 5 tessellation, as well as the Rice1995
tessellation, can each be generated by either one of the 18 sided
polygons (hexagonal flowers) formed by the convex pentagonal
tile.

In this model, a player can experience the property for his or
herself and make even more patterns.