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For equilateral zonogons, a -sided one can be tiled by () rhombi.) In this tiling, there is a parallelogram for each pair of slopes of sides in the 2 n {\displaystyle 2n} -sided zonogon. At least three of the zonogon's vertices must be vertices of only one of the parallelograms in any such tiling. [ 5 ]
The Gauss map of any convex polyhedron maps each face of the polygon to a point on the unit sphere, and maps each edge of the polygon separating a pair of faces to a great circle arc connecting the corresponding two points. In the case of a zonohedron, the edges surrounding each face can be grouped into pairs of parallel edges, and when ...
If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264
The polygon is the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices.
A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates ...
For convex polygons one can cut off each vertex in turn, while for concave polygons this requires more care. A general approach that works for non-simple polygons as well would be to choose a line not parallel to any of the sides of the polygon and draw a line parallel to this one through each of the vertices of the polygon.
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In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted). [ 1 ] [ 2 ] Parallelogons have an even number of sides and opposite sides that are equal in length.