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Spherical f-tilings by two non congruent classes of isosceles triangles - I

Ana Maria Reis d'Azevedo Breda orcid id orcid.org/0000-0001-7076-707X ; Department of Mathematics, University of Aveiro, Aveiro, Portugal
Patrícia dos Santos Ribeiro ; Department of Mathematics, E.S.T. Setúbal, Setúbal, Portugal


Puni tekst: engleski pdf 435 Kb

str. 127-149

preuzimanja: 465

citiraj


Sažetak

The theory of f-tilings is related to the theory of isometric foldings, initiated by S. Robertson [8] in 1977.
The study of dihedral f-tilings of the Euclidean sphere
$S^2$ by triangles and r-sided regular polygons was initiated in
2004, where the case r=4$was considered [4]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and r-sided regular polygons, for any $r\ge 5$, was described. Recently, in [2] and [3] a classification of all triangular dihedral spherical f-tilings for which one of the prototiles is an equilateral triangle is given.
In this paper, we extend these results considering the dihedral case of two non congruent isosceles triangles in a particular way of adjacency ending up to a class of $f$-tilings composed by three parametrised families, denoted by $\mathcal{F}_{k, \alpha}$, $\mathcal{E}_{\alpha}$ and $\mathcal{L}_{k}, \; k\geq 3, \; \alpha>\frac{\pi}{2}$, respectively, and one isolated tiling, denoted by $\mathcal{G}$.
The combinatorial structure including the symmetry group of each
tiling is also given.
Dawson and Doyle in [6], [7] have also been working on spherical tilings, relaxing the edge to edge condition.

Ključne riječi

Dihedral f-tilings; isometric foldings; symmetry groups

Hrčak ID:

82991

URI

https://hrcak.srce.hr/82991

Datum izdavanja:

12.6.2012.

Posjeta: 925 *