Dragon square

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convex dragon square
concave dragon square

A dragon square (also dragon or deltoid ) is a flat square ,


  • that has two pairs of adjacent sides of equal length.

Both definitions are equivalent.

Often, only which is convex form of the deltoids called kite quadrilateral and the concave shape as arrow square or wind bird quadrilateral . The name dragon square refers to the shape of many kites .

A special dragon square is the rhombus . It is an equilateral deltoid .


The following applies to every dragon square (see illustration):

For every convex dragon square the following applies:

A tangent square is a dragon square if and only if one of the following conditions is met:


Mathematical formulas for the dragon square
Side lengths
Length of the diagonal

(see cosine law ,
Heron's theorem )

Inscribed radius
Interior angle

(see cosine law )


An inclined dragon square is a flat square in which one of the diagonals is halved by the other. Such a square is sometimes called crooked . In the case of an inclined dragon square, the diagonals are not necessarily orthogonal to one another. In this sense, the kite square is a straight kite . For the inclined dragon square, a generalized formula for the area applies via the cross product .

A square is a crooked kite if it can be broken down into four equal triangles from an inner point with straight connections to the four corners .

Parquet with dragon squares

Some special tiling contain dragon squares. The Penrose parquet flooring is particularly well known .

Polyhedron with dragon squares

Some polyhedra have kite quadrilaterals as faces . The surface of the deltoidal icositetrahedron and deltoidal hexacontahedron , two Catalan solids , consists of congruent dragon squares.

The rhombohedron , the rhombic dodecahedron, and the rhombic triacontahedron even have diamonds as side faces . The polyhedra mentioned are rotationally symmetrical , ie they can be mapped onto themselves by rotating about certain axes of rotation .

Individual evidence

  1. Curriculum - preparatory courses for work teachers
  2. Martin Josefsson: When is a Tangential Quadrilateral a Kite? , Forum Geometricorum
  3. ^ Dragon Quadrilaterals , Mathematics, TU Freiberg
  4. Jürgen Köller: Hierarchy of the squares , mathematical handicrafts
  5. Hans Walser: Viereck-Viertelung

Web links

Commons : Drachenviereck  - Collection of pictures, videos and audio files
Wiktionary: Drachenviereck  - explanations of meanings, word origins, synonyms, translations