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Hutton's definitions in 1795 [4]. The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (trapezia [5] literally 'table', itself from τετράς (tetrás) 'four' + πέζα (péza) 'foot ...
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
Any non-self-crossing quadrilateral that has an axis of symmetry must be either a kite, with a diagonal axis of symmetry; or an isosceles trapezoid, with an axis of symmetry through the midpoints of two sides. These include as special cases the rhombus and the rectangle respectively, and the square, which is a special case of both. [1]
A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles), and therefore has all ...
A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]
Isomorphic quadrilaterals. In Euclidean geometry, two shapes that are not similar can nonetheless share a common structure. For example, a square and a trapezoid both comprise an alternating chain of four vertices and four sides, which makes them quadrilaterals. They are said to be isomorphic or “structure preserving”.
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The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.