One of them is a tiling by a right kite, with 60°, 90°, and 120° angles. There are only eight polygons that can tile the plane in such a way that reflecting any tile across any one of its edges produces another tile a tiling produced in this way is called an edge tessellation. Among all the bicentric quadrilaterals with a given two circle radii, the one with maximum area is a right kite. Because they circumscribe one circle and are inscribed in another circle, they are bicentric quadrilaterals. That is, for these kites the two equal angles on opposite sides of the symmetry axis are each 90 degrees. the kites that can be inscribed in a circle) are exactly the ones formed from two congruent right triangles. The kites that are also cyclic quadrilaterals (i.e. By avoiding the need to treat special cases differently, this hierarchical classification can help simplify the statement of theorems about kites.Ī kite with three equal 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras. The remainder of this article follows a hierarchical classification, in which rhombi, squares, and right kites are all considered to be kites. For the same reason, with a partitioning classification, shapes meeting the additional constraints of other classes of quadrilaterals, such as the right kites discussed below, would not be considered to be kites. However, with a partitioning classification, rhombi and squares are not considered to be kites, and it is not possible for a kite to be equilateral or equiangular. According to this classification, every equilateral kite is a rhombus, and every equiangular kite is a square. With a hierarchical classification, a rhombus (a quadrilateral with four sides of the same length) or a square is considered to be a special case of a kite, because it is possible to partition its edges into two adjacent pairs of equal length. It is possible to classify quadrilaterals either hierarchically (in which some classes of quadrilaterals are subsets of other classes) or as a partition (in which each quadrilateral belongs to only one class). The deltoidal trihexagonal tiling is made of identical kite faces, with 60-90-120 degree internal angles.
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