Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II

Ana BREDA, Robert DAWSON, Patrícia RIBEIRO

Acta Mathematica Sinica ›› 2014, Vol. 30 ›› Issue (8) : 1435-1464.

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Acta Mathematica Sinica ›› 2014, Vol. 30 ›› Issue (8) : 1435-1464. DOI: 10.1007/s10114-014-3302-5
Articles

Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II

  • Ana BREDA1, Robert DAWSON2, Patrícia RIBEIRO3
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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.

Key words

Spherical tilings / dihedral / triangulations / f-tilings / spherical trigonometry

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Ana BREDA, Robert DAWSON, Patrícia RIBEIRO. Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II. Acta Mathematica Sinica, 2014, 30(8): 1435-1464 https://doi.org/10.1007/s10114-014-3302-5

References

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Funding

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
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