This paper presents our preliminary results on regular meshes in which all faces have the same size and all vertices have the same valence. A regular mesh is denoted by (n, m, g) where n is the number of the sides of faces, m is the valence of vertices and g is the genus of the mesh. For g = 0, regular meshes include regular platonic solids, all two sided polygons. For g = 1 regular meshes include regular tilings of infinite plane. Our work shows that there exist infinitely many regular meshes for g > 1. Moreover, we have constructive proofs that describe how to create high genus regular meshes that consist of triangles and quadrilaterals (3,m,g) and (4,m,g). Copyright 2005 by the Association for Computing Machinery, Inc.
name of conference
Proceedings of the 2005 ACM symposium on Solid and physical modeling
