Eurípedes Alves da SILVA[1]

§    ABSTRACT: By a monohedral plane tiling à we mean one in which each tile is congruent (directly or reflectively) to one fixed set P, called a prototile ofà . We say that the prototile P admits the tiling à . A prototile admiting, up to congruence, precisely r monohedral tilings is said to be r-morphic. For it positive integer r, r £ 10, there exists a r-morphic prototile ( Fontaine & Martin (1983a 1983b, 1984 a and 1984b) , but the existence of r-morphic prototiles remains open for r > 10. Monomorphic prototiles are common, but polymorphic prototiles, even for r =2 or r =3, are harder to find. In this paper we apply the fitting methodology introduced by Barbosa (1993) to get a monohedral hexamorphic prototile different from the one presented by Fontaine & Martin. As far as we know, there is no other references about the existence of a monohedral hexamorphic prototile.

§    KEYWORDS: Monohedral plane tilings; monohedral polymorphic prototiles; polymorphic transformations.




[1]Departamento de Matemática - Instituto de Biociências , Letras e Ciências Exatas - UNESP - São José do Rio Preto - SP - Brasil.