IJPAM: Volume 58, No. 2 (2010)

LOOPS OF POLYGONS

Jaime Rangel-Mondragon$^1$, Arturo Gonzalez-Gutierrez$^2$
$^1$Facultad de Informatica
Universidad Autonoma de Queretaro
C.P. 76010, Queretaro, Qro., MEXICO
e-mail: jrangel@uaq.mx
$^2$Department of Computer Science
University of California
Santa Barbara, CA 93106, USA
e-mail: aglez@cs.ucsb.edu


Abstract.A loop of polygons is a planar arrangement of congruent non overlapping regular polygons in which each polygon has a common edge with exactly two other polygons. A loop encloses an equilateral polygon (not necessarily convex or equiangular but we will require it to be not self-intersecting and of positive area) that we will refer to as the window of the loop. We conduct an exhaustive computational search for all loops of polygons or \(n\)-gons for $3 \leq n \leq 10$ and small values of the perimeter of their windows. The stages leading to the generation and display of the loops were implemented in Mathematica.

Received: November 2, 2009

AMS Subject Classification: 51M15, 52C45, 68R05

Key Words and Phrases: loops of polygons, recursion, algorithms, computational geometry, combinatorial geometry

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 2