Regular Polyhedral Lattices of Genus 2: 11 Platonic Equivalents?

Year: 2010 Authors: Dirk Huylebrouck

Core claim

Genus-2 regular polyhedral lattices satisfying Euler’s formula are limited to 11 Schläfli cases, and several can be modeled as Platonic lookalikes with Zometool or virtual constructions.

Topics

Euler’s formula, genus 2 lattices, hyperbolic geometry, Platonic solids

Domains

topology, polyhedral combinatorics, hyperbolic geometry, architectural geometry, 3D model making, visualization

Methods

spreadsheet enumeration, case classification, physical modeling, virtual modeling

Media

Zometool, vZome, crocheted models, newspaper strings

Source status

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