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Hyperbolic polygons and NEC groups

Published online by Cambridge University Press:  24 October 2008

J. J. Etayo  and
E. Martínez
J. J. Etayo
Affiliation:
Departamento de Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040-Madrid, Spain
E. Martínez
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, U.N.E.D., 28040-Madrid, Spain
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Extract

Beardon [1] gave a procedure for constructing a polygon with prescribed angles. For each ordered set of angles Beardon's polygon is unique up to congruence. The polygon obtained this way has an inscribed circle. It is possible to obtain by means of these polygons a fundamental region for a non-Euclidean crystallographic (NEC) group with a given signature having equal angles in each of the cycles: see [5]. In [5] the minimal number of sides of a convex fundamental region of an NEC group is calculated, and regions are explicitly obtained achieving the bound.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 261 - 272
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

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