Spherical f-tilings by two noncongruent classes of isosceles triangles-II

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• 作者：Ana Breda (1)
  Robert Dawson (2)
  Patrícia Ribeiro (3)
  
• 关键词：Spherical tilings ; dihedral ; triangulations ; f ; tilings ; spherical trigonometry ; 52C20 ; 05B45 ; 52C30
• 刊名：Acta Mathematica Sinica
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：30
• 期：8
• 页码：1435-1464
• 全文大小：725 KB
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  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), 1013-032 (2012) CrossRef
  5. Breda, A.: A class of tilings of / S ₂. / Geometriae Dedicata, 44, 241-53 (1992)
  6. Breda, A., Ribeiro, P.: Spherical / f-tilings by two non congruent classes of isosceles triangles -I. / Math. Comm., 17, 127-49 (2012)
  7. Breda, A., Ribeiro, P., Santos, A.: A class of spherical dihedral / f-tilings. / European J. Combin., 30(1), 119-32 (2009) CrossRef
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  9. Breda, A., Santos, A.: Dihedral / f-tilings of the sphere by spherical triangles and equiangular well centered quadrangles. / Beitr?ge Algebra Geometrie, 45, 441-61 (2004)
  10. Dawson, R.: Tilings of the sphere with isosceles triangles. / Discrete Comput. Geom., 30, 467-87 (2003) CrossRef
  11. Dawson, R., Doyle, B.: Tilings of the sphere with right triangles I: The asymptotically right families. / Electronic J. Combin., 13, #R48 (2006)
  
• 作者单位：Ana Breda (1)
  Robert Dawson (2)
  Patrícia Ribeiro (3)
  
  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 Setúbal, Polytechnic Institute of Setúbal, 2910-761, Setúbal, Portugal
  
• ISSN：1439-7617

文摘

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 {ie?} m , m ?2, m ?? F k , k ?4, k ??and two sporadic tilings denoted by G and H.