Skew polygon
Encyclopedia
In geometry
, a skew polygon is a polygon
whose vertices do not lie in a plane. Skew polygons must have at least 4 vertices
.
A regular skew polygon is a skew polygon with equal edge lengths and which is vertex-transitive
.
The interior surface (or area) of such a polygon is not uniquely defined, although this can be considered as a minimal surface
problem like the form of a soap film inside of a wire frame.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a skew polygon is a 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...
whose vertices do not lie in a plane. Skew polygons must have at least 4 vertices
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
.
A regular skew polygon is a skew polygon with equal edge lengths and which is vertex-transitive
Vertex-transitive
In geometry, a polytope is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same...
.
The interior surface (or area) of such a polygon is not uniquely defined, although this can be considered as a minimal surface
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....
problem like the form of a soap film inside of a wire frame.
See also
- Regular skew polyhedronRegular skew polyhedronIn geometry, the regular skew polyhedra are generalizations to the set of regular polyhedron which include the possibility of nonplanar faces or vertex figures....
- Infinite skew polyhedronInfinite skew polyhedronIn geometry, an infinite skew polyhedron is an extension of the idea of a polyhedron, consisting of regular polygon faces with nonplanar vertex figures, allowing the figure to extend indefinitely without folding round to form a closed surface....
- Petrie polygonPetrie polygonIn geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every consecutive sides belong to one of the facets...
- Apeirogon#Skew forms