The kites are the quadrilaterals that have an axis of symmetry along one of their diagonals.

One diagonal bisects a pair of opposite angles.

One diagonal is a line of symmetry (it divides the quadrilateral into two congruent triangles that are mirror images of each other).

(In the concave case it is the extension of one of the diagonals.)

One diagonal is the perpendicular bisector of the other diagonal.

Two disjoint pairs of adjacent sides are equal (by definition).

The concave case is called a dart.Ī quadrilateral is a kite if and only if any one of the following conditions is true: The tiling that it produces by its reflections is the deltoidal trihexagonal tiling.Įxample convex and concave kites. 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). It has 10 faces on the polar axis with 10 faces following the equator.The deltoidal trihexagonal tiling is made of identical kite faces, with 60-90-120 degree internal angles.

The rhombic icosahedron is a polyhedron composed of 20 rhombic faces, of which three, four, or five meet at each vertex.

The rhombic enneacontahedron is a polyhedron composed of 90 rhombic faces, with three, five, or six rhombi meeting at each vertex.It is nonconvex with 60 golden rhombic faces with icosahedral symmetry. The rhombic hexecontahedron is a stellation of the rhombic triacontahedron.The great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces.

The rhombic triacontahedron is a convex polyhedron with 30 golden rhombi (rhombi whose diagonals are in the golden ratio) as its faces.The rhombic dodecahedron is a convex polyhedron with 12 congruent rhombi as its faces.A rhombohedron (also called a rhombic hexahedron) is a three-dimensional figure like a cuboid (also called a rectangular parallelepiped), except that its 3 pairs of parallel faces are up to 3 types of rhombi instead of rectangles.Three-dimensional analogues of a rhombus include the bipyramid and the bicone as a surface of revolution.Ĭonvex polyhedra with rhombi include the infinite set of rhombic zonohedrons, which can be seen as projective envelopes of hypercubes.Identical rhombi can tile the 2D plane in three different ways, including, for the 60° rhombus, the rhombille tiling.One of the five 2D lattice types is the rhombic lattice, also called centered rectangular lattice.K = p ⋅ q 2 This is a special case of the superellipse, with exponent 1. Quadrilateral, trapezoid, parallelogram, kite

Geometry properties of a kite