Spherical folding tessellations by kites and isosceles triangles IV

Abstract

The classification of the dihedral folding tessellations of the sphere and the plane whose prototiles are a kite and an equilateral triangle were obtained in [1]. Recently, this classification was extended to isosceles triangles so that the classification of spherical folding tesselations by kites and isosceles triangles in three cases of adjacency was presented in [2,3,4]. In this paper we finalize this classification presenting all the dihedral folding tessellations of the sphere by kites and isosceles triangles in the remaining three cases of adjacency, that consists of five sporadic isolated tilings. A list containing these tilings including its combinatorial structure is presented in Table 1.

Geometric and combinatorial structure of a class of spherical folding tessellations - I

“…Concerning dihedral folding tilings by kites and an equilateral or isosceles triangle, the classification was obtained recently, see [1], [2], [3], [4]. In this paper we initiate the classification of dihedral folding tilings of the sphere by kites and scalene triangles: we shall obtain all the dihedral f-tilings of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle.…”