In Search of Demiregular Tilings

Helmer Aslaksen
Bridges London: Mathematics, Music, Art, Architecture, Culture (2006)
Pages 533–536


Many books on mathematics and art discuss a topic called demiregular tilings and claim that there are 14 such tilings. However, many of them give different lists of 14 tilings! In this paper we will compare the lists from some standard references that give a total of 18 such tilings. We will also show that unless we add further restrictions, there will in fact be infinitely many such tilings. The “fact” that there are 14 demiregular tilings has been repeated by many authors. The goal of this paper is to put an end to the concept of demiregular tilings.