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The shape of the snowflake is determined broadly by the temperature and humidity at which it is formed. [8] Rarely, at a temperature of around −2 °C (28 °F), snowflakes can form in threefold symmetry — triangular snowflakes. [9] Most snow particles are irregular in form, despite their common depiction as symmetrical.
The symmetry group of a snowflake is D 6, a dihedral symmetry, the same as for a regular hexagon.. In mathematics, a dihedral group is the group of symmetries of a regular polygon, [1] [2] which includes rotations and reflections.
Fivefold symmetry is found in the echinoderms, the group that includes starfish, sea urchins, and sea lilies. [31] Among non-living things, snowflakes have striking sixfold symmetry; each flake's structure forms a record of the varying conditions during its crystallization, with nearly the same pattern of growth on each of its six arms. [32]
A snowflake consists of roughly 10 19 water molecules which are added to its core 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. As a result, snowflakes differ from each other though they follow similar patterns. [17 ...
An early classification of snowflakes by Israel Perkins Warren. [2] Snow was described in China, as early as 135 BCE in Han Ying's book Disconnection, which contrasted the pentagonal symmetry of flowers with the hexagonal symmetry of snow. [3] Albertus Magnus proved what may be the earliest detailed European description of snow in 1250.
Fivefold symmetry is found in the echinoderms, including starfish, sea urchins, and sea lilies. [2]: 64–65 Among non-living things, snowflakes have striking sixfold symmetry: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms.
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An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6] An object has rotational symmetry if the object can be rotated about a fixed point (or in 3D about a line) without changing the overall shape. [7]