Skip to main content
SpringerLink
Log in

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

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

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 {ieɛ}m, m ≥ 2, m ∈ ℕ, F k, k ≥ 4, k ∈ ℕ and two sporadic tilings denoted by G and H.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agaoka, Y., Ueno, Y.: Classification of tilings of the 2-dimensional sphere by congruent triangles. Hiroshima Math. J., 32, 463–540 (2002)

    MATH  MathSciNet  Google Scholar 

  2. Agaoka, Y., Ueno, Y.: Examples of spherical tilings by congruent quadrangles. Mem. Fac. Integrated Arts and Sci., Hiroshima Univ. Ser. IV, 27, 135–144 (2001)

    Google Scholar 

  3. Avelino, C., Santos, A.: Spherical f-tilings by triangles and r-sided regular polygons, r ≥ 5. Electr. J. Combin., 15(1), #R22 (2008)

    MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Breda, A.: A class of tilings of S 2. Geometriae Dedicata, 44, 241–253 (1992)

    MATH  MathSciNet  Google Scholar 

  6. Breda, A., Ribeiro, P.: Spherical f-tilings by two non congruent classes of isosceles triangles — I. Math. Comm., 17, 127–149 (2012)

    MATH  Google Scholar 

  7. Breda, A., Ribeiro, P., Santos, A.: A class of spherical dihedral f-tilings. European J. Combin., 30(1), 119–132 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Google Scholar 

  9. Breda, A., Santos, A.: Dihedral f-tilings of the sphere by spherical triangles and equiangular well centered quadrangles. Beiträge Algebra Geometrie, 45, 441–461 (2004)

    Google Scholar 

  10. Dawson, R.: Tilings of the sphere with isosceles triangles. Discrete Comput. Geom., 30, 467–487 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dawson, R., Doyle, B.: Tilings of the sphere with right triangles I: The asymptotically right families. Electronic J. Combin., 13, #R48 (2006)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Ana Breda

  2. Department of Mathematics and Computing Science, Saint Mary’s University Halifax, Nova Scotia, B3H 3C3, Canada

    Robert Dawson

  3. Department of Mathematics, EST Setúbal, Polytechnic Institute of Setúbal, 2910-761, Setúbal, Portugal

    Patrícia Ribeiro

Authors
  1. Ana Breda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Dawson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patrícia Ribeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ana Breda.

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Breda, A., Dawson, R. & Ribeiro, P. Spherical f-tilings by two noncongruent classes of isosceles triangles-II. Acta. Math. Sin.-English Ser. 30, 1435–1464 (2014). https://doi.org/10.1007/s10114-014-3302-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-014-3302-5

Keywords

MR(2010) Subject Classification

Search

Navigation