This game is also known as Stomachion and is described in this page:
http://www.mcs.drexel.edu/~crorres/Archimedes/Stomachion/intro.html
By the way, this is a part of an excellent page about Archimedes.
Jaime
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Jaime Carvalho e Silva
Departamento de Matematica, Universidade de Coimbra
Apartado 3008, 3000 Coimbra, PORTUGAL
Phone(office): 351-39-791199 (pbx):351-39-791150 Fax: 351-39-832568
WWW home page: http://www.mat.uc.pt/~jaimecs/pessoal/
NONIUS: http://www.mat.uc.pt/~jaimecs/
History page: http://www.mat.uc.pt/~jaimecs/indexhm.html
"O Mocho": http://softciencias.ccg.uc.pt/mocho/