A closed figure composed of three or more line segments on the same plane but not on the same straight line, which is connected end to end and does not intersect, is called a polygon. A figure composed of many line segments on different planes that are connected end to end and do not intersect is also called a polygon, which is a generalized polygon.
There are at least three line segments that make up a polygon, and a triangle is the simplest polygon. Each line segment that constitutes a polygon is called an edge of the polygon; The common endpoint of two adjacent line segments is called the vertex of the polygon; The angle formed by two adjacent sides of a polygon is called the inner angle of the polygon; The line segment connecting two nonadjacent vertices of a polygon is called the diagonal of the polygon.
The angle formed by the extension line with one side of the inner angle of a polygon opposite to the other side is called the outer angle of the polygon.
Take an outer corner of the polygon at each vertex, and their sum is called the sum of the outer corners of the polygon.
Polygons can also be divided into regular polygons and non-regular polygons. Regular polygons have equal sides and equal internal angles.
Polygons are divided into planar polygons and spatial polygons. All vertices of a planar polygon are on the same plane, and at least one vertex of a spatial polygon is not on the same plane with other vertices.
Polygons can also be divided into convex polygons and concave polygons. All convex polygons are planar polygons (planar polygons are not equal to convex polygons, but also include planar concave polygons), but concave polygons are not all spatial polygons, but there are also planar concave polygons.
The sum of finite points A 1, A2, A3, …, An- 1, An and line segments A 1A2, A2A3, …, An- 1An is called a polyline. A 1 and an are called the endpoints of this polyline;
A2, A3, …, An- 1 are called vertices of polylines; A 1A2, A2A3, …, An- 1An are line segments called polylines. If the endpoints and vertices of a polyline are not on the same plane, it is called a spatial polyline. If each vertex and both ends are on the same plane.
This is called a planar polyline. A broken line whose two ends coincide is called a polygon. Polygons composed of spatial polylines are called spatial polygons; A polygon composed of planar polylines is called a planar polygon. If both ends of a polyline A 1A2A3…An- 1An coincide with An.
It is a polygon A1A2A3 … an-1an; A 1A2, A2A3, …, An- 1An are called the edges of a polygon; ∠ana 1 a2,∠a 1a2a 3 .
... called the corner of a polygon; A 1, A2, A3, …, An- 1, An is called the vertex of this polygon. According to the number of sides, planar polygons can be divided into triangles, quadrilaterals, pentagons, hexagons and so on.