IJPAM: Volume 58, No. 2 (2010)



Universidad Autonoma de Queretaro
C.P. 76010, Queretaro, Qro., MEXICO
e-mail: [email protected]

University of California
Santa Barbara, CA 93106, USA
e-mail: [email protected]
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
-gons for
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