This article is cited in 1 paper

Geometry and topology

Convex pentagons which tile the plane (types: 11112, 11122)

O. G. Bagina

Kemerovo State University

Abstract: We consider the problem of classifying the convex pentagons that tile the plane edge-to-edge. It is proved that in each such tiling of the plane by pentagons, there exists a tile whose set of vertex degrees can be one of the following: (3,3,3,3,3), (3,3,3,3,4), (3,3,3,3,5), (3,3,3,3,6), (3,3,3,4,4). This provides the possibility of searching which finally leads to exhaustive classification of such pentagons. We consider convex pentagons types 11112, 11122.

Keywords: convex pentagon, tiling the plane, plane.

UDC: 519.148

MSC: 52C20

Received May 25, 2012, published November 5, 2012