'Does the geometric design of centrioles imply their function? Several principles of construction of a microscopically small device for locating the directions of signal sources in microscopic dimensions: it appears that the simplest and smallest device that is compatible with the scrambling influence of thermal fluctuations, as are demonstrated by Brownian motion, is a pair of cylinders oriented at right angles to each other. Centrioles locate the direction of hypothetical signals inside cells' (Albrecht-Buehler G, Cell Motil, 1:237-245; 1981).Despite a century of devoted efforts (articles on the centrosome always begin like this) its role remains vague and nebulous: does the centrosome suffer from bad press? Likely it does, it has an unfair image problem. It is dispensable in mitosis, but a fly zygote, artificially deprived of centrosomes, cannot start its development; its sophisticated architecture (200 protein types, highly conserved during evolution) constitutes an enigmatic puzzle; centrosome reduction in gametogenesis is a challenging brainteaser; its duplication cycle (only one centrosome per cell) is more complicated than chromosomes. Its striking geometric design (two ninefold symmetric orthogonal centrioles) shows an interesting correspondence with the requirements of a cellular compass: a reference system organizer based on a pair of orthogonal goniometers; through its two orthogonal centrioles, the centrosome may play the role of a cell geometry organizer: it can establish a finely tuned geometry, inherited and shared by all cells. Indeed, a geometrical and informational primary role for the centrosome has been ascertained in Caenorhabditis elegans zygote: the sperm centrosome locates its polarity factors. The centrosome, through its aster of microtubules, possesses all the characteristics necessary to operate as a biophysical geometric compass: it could recognize cargoes equipped with topogenic sequences and drive them precisely to where they are addressed (as hypothesized by Albrecht-Buehler nearly 40 years ago). Recently, this geometric role of the centrosome has been rediscovered by two important findings; in the Kupffer's vesicle (the laterality organ of zebrafish), chiral cilia orientation and rotational movement have been described: primary cilia, in left and right halves of the Kupffer's vesicle, are symmetrically oriented relative to the midline and rotate in reverse direction. In mice node (laterality organ) left and right perinodal cells can distinguish flow directionality through their primary cilia: primary cilium, ninefold symmetric, is strictly connected to the centrosome that is located immediately under it (basal body). Kupffer's vesicle histology and mirror behaviour of mice perinodal cells suggest primary cilia are enantiomeric geometric organelles. What is the meaning of the geometric design of centrioles and centrosomes? Does it imply their function?