Geometric and combinatorial structure of a class of spherical folding tessellations — I

A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tes...

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Bibliographic Details
Published inCzechoslovak mathematical journal Vol. 67; no. 4; pp. 891 - 918
Main Authors Avelino, Catarina P., Santos, Altino F.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects
Analysis
Classification
Combinatorial analysis
Convex and Discrete Geometry
Folding
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Tiling
Triangles
20B35
52C20
symmetry group
52B05
combinatorial propertie
spherical trigonometry
dihedral f-tiling
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Summary:A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed. The combinatorial structure of each tiling is also analysed.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2017.0610-15