Symmetry (Dec 2021)

GomJau-Hogg’s Notation for Automatic Generation of k-Uniform Tessellations with ANTWERP v3.0

  • Valentin Gomez-Jauregui,
  • Harrison Hogg,
  • Cristina Manchado,
  • Cesar Otero

DOI
https://doi.org/10.3390/sym13122376
Journal volume & issue
Vol. 13, no. 12
p. 2376

Abstract

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Euclidean tilings are constantly applied to many fields of engineering (mechanical, civil, chemical, etc.). These tessellations are usually named after Cundy & Rollett’s notation. However, this notation has two main problems related to ambiguous conformation and uniqueness. This communication explains the GomJau-Hogg’s notation for generating all the regular, semi-regular (uniform) and demi-regular (k-uniform, up to at least k = 3) in a consistent, unique and unequivocal manner. Moreover, it presents Antwerp v3.0, a free online application, which is publicly shared to prove that all the basic tilings can be obtained directly from the GomJau-Hogg’s notation.

Keywords