From teaching experience. XV. Crystallographic borders and phyllotaxis

Phyllotaxis is an orderly arrangement of leaves on plant stems and branches. Its origin is that each species in the course of evolution optimized the light flux for each leaf. The found optimum was fixed in the genotype and became a phenotypic trait. The possibility to use the crystallographic ideas in botany was shown by A. Bravais. The given paper proposes to describe the arrangement of leaves on a horizontal branch in terms of the theory of borders. All seven possible types of borders are found to be theoretically consistent. The suggested nomenclature in terms of symmetry operations strictly fixes straight and oblique arrangement of symmetrical and asymmetrical leaves on branches. Botanical prototypes have been established for all types of borders.