Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles

Abstract

The study of spherical dihedral f-tilings when the prototiles are two
noncongruent isosceles triangles was started in two previous papers. Here,
we complete the classication, characterizing the f-tilings that satisfy the
remaining case of adjacency. As it will be shown, this class is composed by
two three-parameter families denoted by An;m; and Bn;m; and a related
four-parameter family denoted by Bp;q;p
′
;q
′
, where p > p
′ 0; q
′
> q 0;
two isolated tilings denoted by P and Q; and six distinct discrete families
denoted by J k;Lk; Mk;Nk(k 3); and Fk;Kk with k 4.