The stages of radial, spiral, and bilateral cleavage, including blastula, are considered as polyhedrons and projections of polyhedrons onto a plane: Wenn, Schlegel, and Euler projections. The blastula spatial organization is characterized by face numerals and Euler characteristics, as well by symmetry groups. The classes of equivalence of polyhedrons have been considered: duality and equal composition. The correspondence between different types of cleavage has been established by shift transformation on Schlegel projections and turn on a spherical noneuclidean surface. Determination of the prospective significance of blastomeres during cleavage was compared with the dichotomous division of the general notion in logic. This in view, the Wenn diagram of four figures has been reflected onto the sphere surface. Blastula faceting is interpreted as a reflection of hereditary information about the prospective significance of blastomeres onto a spherical surface. Topologically, the reflection represents a transformation of the linear orderliness of information contained in the genome into a two-dimensional orderliness of prospective properties on the blastula noneuclidean surface. Therefore, the elements of blastula symmetry can be considered as self in the sense of Pierre Curie principle. Cleavage stages are living colloid crystals.
Russian Journal of Developmental Biology – Springer Journals
Published: Jul 17, 2006
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