Surface Covering with Regular Polygons: A Brief Discussion

Abstract

In this article a limelight has been fallen on some of the possible ways to cover a surface (flat, curved and closed) by some of the regular polygons. To cover a two dimensional surface with regular polygons; equilateral triangle, square, and regular hexagon can be found to be used separately but regular pentagon, heptagon and other higher regular polygons cannot be used separately for this purpose. A curved surface can be found to be covered with regular polygons such as equilateral triangle, square, and regular pentagon separately but cannot be covered with hexagons or other higher regular polygons unless one or more polygons having size less than six are present. For covering a closed surface that is to make a curved surface closed it is found that equilateral triangle, square, and regular pentagon can be employed separately or various combination thereof. Regular polygons having size six or more in addition with regular polygons having size less than six can be used to cover a closed surface in a planned way governed by Euler’s polyhedron formula.