Voronoi Tessellations and the Shannon Entropy of the Pentagonal Tilings.

Edward Bormashenko, Irina Legchenkova, Mark Frenkel, Nir Shvalb, Shraga Shoval

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Article in Entropy (Basel, Switzerland), 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

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1citing papers in PubMed

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1 citing paper in PubMed.

Shannon Entropy of Ramsey Graphs with up to Six Vertices.Entropy (Basel, Switzerland) · 2023
Article

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5 authors.

Edward BormashenkoChemical Engineering Department, Engineering Faculty, Ariel University, P.O.B. 3, Ariel 407000, Israel.ORCID 0000-0003-1356-2486

Irina LegchenkovaChemical Engineering Department, Engineering Faculty, Ariel University, P.O.B. 3, Ariel 407000, Israel.ORCID 0000-0002-6384-7570

Mark FrenkelChemical Engineering Department, Engineering Faculty, Ariel University, P.O.B. 3, Ariel 407000, Israel.ORCID 0000-0003-3025-6130

Nir ShvalbDepartment of Mechanical Engineering & Mechatronics, Faculty of Engineering, Ariel University, P.O.B. 3, Ariel 407000, Israel.ORCID 0000-0001-8246-3727

Shraga ShovalDepartment of Industrial Engineering and Management, Faculty of Engineering, Ariel University, P.O.B. 3, Ariel 407000, Israel.ORCID 0000-0002-0582-4821

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

We used the complete set of convex pentagons to enable filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons, and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group. However, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.

Indexed as

iso-symmetrical transitionsMarjorie Rice Tilingpentagonal tilingShannon entropyVoronoi tessellation

Identifiers

PMID36673233

DOI10.3390/e25010092

PMCPMC9857938

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.