## Kodai Mathematical Journal

- Kodai Math. J.
- Volume 27, Number 1 (2004), 88-104.

### Generic fundamental polygons for surfaces of genus three

Jacek Ch\k{a}dzy\'{n}ski and Gou Nakamura

#### Abstract

In the study of extremal surfaces it is important to see the side-pairings of the generic fundamental polygons. For the regular 30-gon in the hyperbolic plane it is known that there are 1726 side-pairing patterns to make a compact surface of genus three. If we consider the mirror images of these patterns, then there are essentially 927 patterns. In the present paper we give the 927 side-pairing patterns completely.

#### Article information

**Source**

Kodai Math. J. Volume 27, Number 1 (2004), 88-104.

**Dates**

First available in Project Euclid: 21 May 2004

**Permanent link to this document**

http://projecteuclid.org/euclid.kmj/1085143791

**Digital Object Identifier**

doi:10.2996/kmj/1085143791

**Mathematical Reviews number (MathSciNet)**

MR2042793

#### Citation

Ch\k{a}dzy\'{n}ski, Jacek; Nakamura, Gou. Generic fundamental polygons for surfaces of genus three. Kodai Math. J. 27 (2004), no. 1, 88--104. doi:10.2996/kmj/1085143791. http://projecteuclid.org/euclid.kmj/1085143791.