Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010)

Pages 199–206 Regular Papers

The paper observes Euler's formula for genus 2 regular polyhedral
lattices is obeyed by *at most* 11 cases of the Schläfli symbol
{p,q}, where p is the number of edges of each face and q the number
of faces meeting at each vertex. *At least* one example is given for
the 'first' 6 cases, but not for their 5 'duals'. The examples are
known from various sources, but their present classification suggests
they are lookalikes of classical Platonic equivalents. An 'artistic'
corollary is the observation that hyperbolic geometry models can
be constructed using Zometool.

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