, Volume 11, Issue 2, pp 145-155

Clean triangulations

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Abstract

A polyhedron on a surface is called a clean triangulation if each face is a triangle and each triangle is a face. LetS p (resp.N p ) be the closed orientable (resp. nonorlentable) surface of genusp. If τ(S) is the smallest possible number of triangles in a clean triangulation ofS, the results are: τ(N 1)=20, τ(S 1)=24, limτ(S p )p −1=4, limτ(N p )p −1=2 forp→∞.