Prismatic surface
Encyclopedia
A prismatic surface is a surface
generated by all the lines that are parallel
to a given line
and intersect a broken line that is not in the same plane as the given line. The broken line is the directrix of the surface; the parallel lines are its generators (or elements). If the broken line is closed (i.e. a closed polygon
), then the surface is a closed prismatic surface.
With regards to crystallography
, a prismatic surface is a single face
of a prismatic form, which is an open form consisting of three, four, or six identical faces related by a symmetry operator.
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
generated by all the lines that are parallel
Parallel (geometry)
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...
to a given line
Line (geometry)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
and intersect a broken line that is not in the same plane as the given line. The broken line is the directrix of the surface; the parallel lines are its generators (or elements). If the broken line is closed (i.e. a closed polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
), then the surface is a closed prismatic surface.
With regards to crystallography
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
, a prismatic surface is a single face
Face (geometry)
In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
of a prismatic form, which is an open form consisting of three, four, or six identical faces related by a symmetry operator.