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Triangulations of the sphere, bitrades and abelian groups

✍ Scribed by Blackburn, Simon R.; McCourt, Thomas A.

Book ID
125348557
Publisher
Springer-Verlag
Year
2014
Tongue
English
Weight
418 KB
Volume
34
Category
Article
ISSN
0209-9683

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πŸ“œ SIMILAR VOLUMES

Latin bitrades, dissections of equilater
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## Abstract Let __T__=(__T__^\*^, __T__^β–΅^) be a spherical latin bitrade. With each __a__=(__a__~1~, __a__~2~, __a__~3~)∈__T__^\*^ associate a set of linear equations __Eq__(__T, a__) of the form __b__~1~+__b__~2~=__b__~3~, where __b__=(__b__~1~, __b__~2~, __b__~3~) runs through __T__^\*^\{__a__}.

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In this paper we analyse a method for triangulating the sphere originally proposed by Baumgardner and Frederickson in 1985. The method is essentially a refinement procedure for arbitrary spherical triangles that fit into a hemisphere. Refinement is carried out by dividing each triangle into four by

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A triangulation is said to be even if each vertex has even degree. For even triangulations, define the N-flip and the P 2 -flip as two deformations preserving the number of vertices. We shall prove that any two even triangulations on the sphere with the same number of vertices can be transformed int