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 A crystal is a solid
composed of atoms arranged in an orderly and repetitive
array. As a crystal grows it accumulates layers of atoms
pulled into the proper arrangement and alignment by the
attracting forces of the atoms already in place. The atoms
of crystals behave in a manner, which is best described
as spherical, as they stack together like spheres and exert
forces upon each other that have spherical qualities.
Many
branches of crystallography consider solids to be built
from the packing together of atoms, which have a spherical
shape. Spheres may be close packed in a triangular pattern
with layers nestled into the depressions formed in the previous
layers, or in a square pattern where consecutive layers
sit directly on top of the previous layer. A polyhedron
defines a set of faces connecting the centers of a set of
spheres. If the center of the spheres are linked together
by lines, a three-dimensional lattice of polyhedra is revealed.
Inside of the lattice, the pattern of points that compose
the polyhedra are identical and exhibit translational symmetry.
When
atomic structures are represented by the faces, vertices,
and edges of polyhedra it is called topological modeling,
as the model shows the symmetry of the geometric elements.
Symmetry is one of the best methods for simplifying study
of the various arrays of atoms which make up crystalline
solids, as it enables the solid to be described in terms
of patterns. If an object has an n-fold axis of symmetry,
it occupies the same positions in space after each angular
rotation of 360 degrees.
In Visual-Synth
a spatial-lattice is used to describe the space of a universe.
The lattice may be packed according to the different spatial-packing
modes and may be subdivided into smaller set of planes called
Plane-Sets. The universe's Plane-Sets may hold any combination
of polyhedra. Each polyhedron in a Plane-Set has a rule
that instructs the polyhedron how to grow, evolve, die,
and respond to its environment.
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