EJMT Abstract

This introductory paper defines a polytile or p-tile as an equilateral polygon with turn angles as multiples of 360°/p, for even p=4, 6, 8…. Polytile notation is offered as a simple way to describe these polygons, with a geometric interpretation as a cycle of edge-to-edge regular p-gons, with vertices centered on each p-gon. A wide range of examples polygons and tilings are shown in this paper to demonstrate a breadth of value. A next paper, part 1b, will formalize the definition and report an enumeration of convex polytiles. Further papers will elaborate topics introduced in this paper including stars, compounds, extending notations, recursively extended polygons, symmetry, naming of polygons, and partial and fractional polytiles which allow one or two unequal edge lengths.