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In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side".
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
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Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. [1] It is not known whether five-sided solutions without holes are possible. [2] Kim's solution has 16 vertices, while some of the pentagon solutions have as few as 11 vertices.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle , [ 3 ] a triangle with two sides having the same length is an isosceles triangle , [ 4 ] [ a ] and a triangle with three different-length sides is a scalene triangle . [ 7 ]
where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.