Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II
Acta Mathematica Sinica, English Series
HOME| ABOUT JOURNAL | EDITORIAL BOARD | FOR AUTHORS| SUBSCRIPTIONS| ADVERTISEMENT| CONTACT US
 
Acta Mathematica Sinica,
Chinese Series
 
   
   
Adv Search »  
Acta Mathematica Sinica, English Series  2014, Vol. 30 Issue (8): 1435-1464    DOI: 10.1007/s10114-014-3302-5
Articles Current Issue | Next Issue | Archive | Adv Search  |   
Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II
Ana BREDA1, Robert DAWSON2, Patrícia RIBEIRO3
1. Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;
2. Department of Mathematics and Computing Science, Saint Mary's University Halifax, Nova Scotia, B3H 3C3, Canada;
3. Department of Mathematics, EST Set磚bal, Polytechnic Institute of Set磚bal, 2910-761 Set磚bal, Portugal
 Download: PDF (674 KB)   HTML ( KB)   Export: BibTeX | EndNote (RIS)      Supporting Info
Abstract In this work, we give a complete classification of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles with certain adjacency pattern. As it will be shown, this class is composed by two discrete families denoted by Em, m≥2, m ∈ N, Fk, k≥4, k ∈ N and two sporadic tilings denoted by G and H.
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Ana BREDA
Robert DAWSON
Patrícia RIBEIRO
Key wordsSpherical tilings   dihedral   triangulations   f-tilings   spherical trigonometry     
Received: 2013-05-21;
Fund: Supported by FEDER funds through COMPETE Operational Programme Factors of Competitiveness (Programa Operacional Factores de Competitividade), by FSE, by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (FCT Fundação para a Ciência e a Tecnologia), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690;supported partially by an NSERC Canada Discovery Grant
Cite this article:   
Ana BREDA,Robert DAWSON,Patrícia RIBEIRO. Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II[J]. Acta Mathematica Sinica, English Series, 2014, 30(8): 1435-1464.
URL:  
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-014-3302-5      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2014/V30/I8/1435
 
[1] Agaoka, Y., Ueno, Y.: Classification of tilings of the 2-dimensional sphere by congruent triangles. HiroshimaMath. J., 32, 463-540 (2002)
[2] Agaoka, Y., Ueno, Y.: Examples of spherical tilings by congruent quadrangles. Mem. Fac. Integrated Artsand Sci., Hiroshima Univ. Ser. IV, 27, 135-144 (2001)
[3] Avelino, C., Santos, A.: Spherical f-tilings by triangles and r-sided regular polygons, r≥5. Electr. J.Combin., 15(1), #R22 (2008)
[4] Avelino, C., Santos, A.: Spherical f-tilings by scalene triangles and isosceles trapezoids, II. Acta Math.Sin., Engl. Series, 28(5), 1013-1032 (2012)
[5] Breda, A.: A class of tilings of S2. Geometriae Dedicata, 44, 241-253 (1992)
[6] Breda, A., Ribeiro, P.: Spherical f-tilings by two non congruent classes of isosceles triangles-I. Math.Comm., 17, 127-149 (2012)
[7] Breda, A., Ribeiro, P., Santos, A.: A class of spherical dihedral f-tilings. European J. Combin., 30(1),119-132 (2009)
[8] Breda, A., Ribeiro, P., Santos, A.: Dihedral f-tilings of the sphere by equilateral and scalene triangles-III.Electronic J. Combin., 15(1), #R147 (2008)
[9] Breda, A., Santos, A.: Dihedral f-tilings of the sphere by spherical triangles and equiangular well centeredquadrangles. Beiträge Algebra Geometrie, 45, 441-461 (2004)
[10] Dawson, R.: Tilings of the sphere with isosceles triangles. Discrete Comput. Geom., 30, 467-487 (2003)
[11] Dawson, R., Doyle, B.: Tilings of the sphere with right triangles I: The asymptotically right families.Electronic J. Combin., 13, #R48 (2006)
No Similar of article
  Copyright 2012 © Editorial Office of Acta Mathematica Sinica
京ICP备05002806号-7