Geometrical motives in the Tetraodontiformes fishes morphology
Geological Institute, Kola Science Centre, RAS
184209 Apatity, id. Fersmaa, 14
e-mail: woyt@geoksc.apatity.ru
Analysis of features of the Ostraciontidae (boxfishes) and Diodontidae (porcupinefishes) families revealed their morphological dualism, also known in combinatorial geometry and crystallography as the dualism of the Dirichlet tiling and that of Delaunay. If we take bases of spines on the body of Diodontidae for the Delaunay points (R, r)-system, the respective Dirichlet tiling will reveal the surface of an Ostraciontidae species being divided into polygonal osseous blades. This fact corroborates taxonomic relationship of the Ostraciontidae and Diodontidae families within the Tetraodontiformes order and indicates the principles of purposefulness in nature, which manifest both in mineral and biological structures. In the course of the present research four specimens of Diodon holocanthus (Diodontidae) were studied and characteristics of the Dirichlet tiling for the surfaces of their bodies were determined.
