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
Integer points in convex polyhedra Integer points in convex polyhedra The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear equations with nonnegative coefficients have" or "how many solutions does an integer linear program have". Counting integer points in polyhedra or other questions about them arise in representation theory, commutative algebra, algebraic geometry, statistics, and computer science. The set of integer points, or, more generally, the set of points of an affine lattice, in a polyhedron is called Z-polyhedron, from the mathematical notation formula_1 or Z for the set of integer