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Open AccessArticle

Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology

Consejo Nacional de Ciencia y Tecnología (CONACYT, Mexico), 03940 Ciudad de Mexico, Mexico
Área de Investigación de Sistemas de Información y Ciencias Computacionales, Universidad Autónoma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico
Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, 76230 Queretaro, Mexico
Author to whom correspondence should be addressed.
Entropy 2018, 20(9), 705;
Received: 28 July 2018 / Revised: 6 September 2018 / Accepted: 7 September 2018 / Published: 14 September 2018
(This article belongs to the Special Issue Biological Statistical Mechanics)
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. View Full-Text
Keywords: pentagon; fivefold morphology; body plan; spatial organization; morphospace pentagon; fivefold morphology; body plan; spatial organization; morphospace
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López-Sauceda, J.; López-Ortega, J.; Laguna Sánchez, G.A.; Sandoval Gutiérrez, J.; Rojas Meza, A.P.; Aragón, J.L. Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology. Entropy 2018, 20, 705.

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