Euler’s Polyhedron Formula for Uniform Tessellations

Year: 2021 Authors: Dirk Huylebrouck

Core claim

Uniform planar tessellations satisfy Euler’s generalized formula with genus 1, so V + F - E = 0.

Topics

Euler characteristic, uniform tessellations, polyhedra, plane graphs, teaching examples

Domains

topology, polyhedral combinatorics, graph theory, tessellation geometry, mathematical art, pattern design, architecture

Methods

counting vertices faces edges, worked tessellation examples, conceptual generalization

Media

square tiling, hexagonal tiling, triangular tiling, truncated trihexagonal tiling, illustrated figures

Source status

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