Snowflake of ice. At that stage, the snowflake has the shape of a minute hexagon. The six "arms" of the snowflake, or dendrites, then grow independently from each of the corners of the hexagon, while either side of each arm grows independently. The microenvironment in which the snowflake grows changes dynamically as the snowflake falls through the cloud and tiny changes in temperature and humidity affect the way in which water molecules attach to the snowflake. Since the micro-environment (and its changes) are very nearly identical around the snowflake, each arm tends to grow in nearly the same way. However, being
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