{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:21:51Z","timestamp":1772252511793,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T00:00:00Z","timestamp":1536883200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based on principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (3 to 10-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs.<\/jats:p>","DOI":"10.3390\/e20090705","type":"journal-article","created":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T10:57:59Z","timestamp":1536922679000},"page":"705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5174-6046","authenticated-orcid":false,"given":"Juan","family":"L\u00f3pez-Sauceda","sequence":"first","affiliation":[{"name":"Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT, Mexico), 03940 Ciudad de Mexico, Mexico"},{"name":"\u00c1rea de Investigaci\u00f3n de Sistemas de Informaci\u00f3n y Ciencias Computacionales, Universidad Aut\u00f3noma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge","family":"L\u00f3pez-Ortega","sequence":"additional","affiliation":[{"name":"\u00c1rea de Investigaci\u00f3n de Sistemas de Informaci\u00f3n y Ciencias Computacionales, Universidad Aut\u00f3noma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gerardo Abel","family":"Laguna S\u00e1nchez","sequence":"additional","affiliation":[{"name":"\u00c1rea de Investigaci\u00f3n de Sistemas de Informaci\u00f3n y Ciencias Computacionales, Universidad Aut\u00f3noma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5578-4389","authenticated-orcid":false,"given":"Jacobo","family":"Sandoval Guti\u00e9rrez","sequence":"additional","affiliation":[{"name":"\u00c1rea de Investigaci\u00f3n de Sistemas de Informaci\u00f3n y Ciencias Computacionales, Universidad Aut\u00f3noma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ana Paola","family":"Rojas Meza","sequence":"additional","affiliation":[{"name":"\u00c1rea de Investigaci\u00f3n de Sistemas de Informaci\u00f3n y Ciencias Computacionales, Universidad Aut\u00f3noma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 Luis","family":"Arag\u00f3n","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica Aplicada y Tecnolog\u00eda Avanzada, Universidad Nacional Aut\u00f3noma de M\u00e9xico, 76230 Queretaro, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,14]]},"reference":[{"key":"ref_1","unstructured":"Hargittai, I. 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