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

Ana Maria Reis d'Azevedo Breda   ORCID icon 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: 295* citiraj
APA 6th Edition
d'Azevedo Breda, A.M.R. i Ribeiro, P.d.S. (2012). Spherical f-tilings by two non congruent classes of isosceles triangles - I. Mathematical Communications, 17 (1), 127-149. Preuzeto s https://hrcak.srce.hr/82991
MLA 8th Edition
d'Azevedo Breda, Ana Maria Reis i Patrícia dos Santos Ribeiro. "Spherical f-tilings by two non congruent classes of isosceles triangles - I." Mathematical Communications, vol. 17, br. 1, 2012, str. 127-149. https://hrcak.srce.hr/82991. Citirano 20.08.2019.
Chicago 17th Edition
d'Azevedo Breda, Ana Maria Reis i Patrícia dos Santos Ribeiro. "Spherical f-tilings by two non congruent classes of isosceles triangles - I." Mathematical Communications 17, br. 1 (2012): 127-149. https://hrcak.srce.hr/82991
Harvard
d'Azevedo Breda, A.M.R., i Ribeiro, P.d.S. (2012). 'Spherical f-tilings by two non congruent classes of isosceles triangles - I', Mathematical Communications, 17(1), str. 127-149. Preuzeto s: https://hrcak.srce.hr/82991 (Datum pristupa: 20.08.2019.)
Vancouver
d'Azevedo Breda AMR, Ribeiro PdS. Spherical f-tilings by two non congruent classes of isosceles triangles - I. Mathematical Communications [Internet]. 2012 [pristupljeno 20.08.2019.];17(1):127-149. Dostupno na: https://hrcak.srce.hr/82991
IEEE
A.M.R. d'Azevedo Breda i P.d.S. Ribeiro, "Spherical f-tilings by two non congruent classes of isosceles triangles - I", Mathematical Communications, vol.17, br. 1, str. 127-149, 2012. [Online]. Dostupno na: https://hrcak.srce.hr/82991. [Citirano: 20.08.2019.]

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

Posjeta: 433 *