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- Title
TRIANGULATIONS OF UNORIENTABLE SURFACES.
- Authors
BROUGHTON, S. ALLEN; BRANDANI DA SILVA, EDUARDO
- Abstract
We consider the question of when an unorientable surface without boundary can be tiled by an (l, m, n) triangle. We desire that the automorphism group of the surface preserving the tiling be “substantial”. We use the well known theory of quasiplatonic surfaces and symmetries of Riemann surfaces to propose a classification algorithm, entirely by finite group calculations. A comprehensive analysis of symmetries of quasiplatonic surfaces in low genus, by hand and by computer, is carried out, yielding triangulations of unoriented surfaces as a byproduct.
- Subjects
AUTOMORPHISM groups; FINITE groups; CLASSIFICATION algorithms; RIEMANN surfaces; TRIANGULATION; TRIANGLES
- Publication
Albanian Journal of Mathematics, 2023, Vol 17, Issue 2, p105
- ISSN
1930-1235
- Publication type
Article
- DOI
10.51286/albjm/1702292327