Snowflake unlikely that any two snowflakes are alike due to the estimated 10 (10 quintillion) water molecules which make up a typical snowflake, which grow at different rates and in different patterns depending on the changing temperature and humidity within the atmosphere that the snowflake falls through on its way to the ground. Snowflakes that look identical, but may vary at the molecular level, have been grown under controlled conditions. Although snowflakes are never completely symmetrical, a non-aggregated snowflake often grows so as to exhibit an approximation of six-fold radial symmetry. The symmetry gets started due to the hexagonal crystalline structure
Five points determine a conic the answer is given in terms of the multiset coefficient, more familiarly the binomial coefficient, or more elegantly the rising factorial, as: This is via the analogous analysis of the Veronese map: "k" points in general position impose "k" independent linear conditions on a variety (because the Veronese map is biregular), and the number of monomials of degree "d" in formula_18 variables ("n"-dimensional projective space has formula_18 homogeneous coordinates) is formula_20 from which 1 is subtracted because of projectivization: multiplying a polynomial by a constant does not change its zeros. In the above formula, the number of points "k" is