Moscow Mathematical Journal

Volume 17, Issue 2, April–June 2017 pp. 191–237.

Spherical Folding Tessellations by Kites and Isosceles Triangles III

Authors: Catarina P. Avelino (1) and Altino F. Santos (2)
Author institution:(1) Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal, CMAT-UTAD, CEMAT-IST-UL
(2) Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal, CMAT-UTAD

Summary:

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 2012 by the authors. In this paper we extend this classification presenting all the dihedral folding tessellations of the sphere by kites and isosceles triangles in a particular case of adjacency that consists of two discrete families denoted by A^k and B^k, k ≥ 3. A list containing these tilings including its combinatorial structure is presented.

2010 Math. Subj. Class. 52C20, 05B45, 52C30, 20B35.

Keywords: Dihedral f-tilings, combinatorial properties, spherical trigonometry, symmetry groups.

Contents Full-Text PDF