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  2. Orthodiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Orthodiagonal_quadrilateral

    A square is a limiting case of both a kite and a rhombus. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem. The square is one such quadrilateral ...

  3. Kite (geometry) - Wikipedia

    en.wikipedia.org/wiki/Kite_(geometry)

    As is true more generally for any orthodiagonal quadrilateral, the area of a kite may be calculated as half the product of the lengths of the diagonals and : [10] =. Alternatively, the area can be calculated by dividing the kite into two congruent triangles and applying the SAS formula for their area.

  4. Uniform polyhedron - Wikipedia

    en.wikipedia.org/wiki/Uniform_polyhedron

    Coxeter, Longuet-Higgins & Miller (1954) define uniform polyhedra to be vertex-transitive polyhedra with regular faces. They define a polyhedron to be a finite set of polygons such that each side of a polygon is a side of just one other polygon, such that no non-empty proper subset of the polygons has the same property.

  5. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Informally: "a box or oblong" (including a square). Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length.

  6. Isosceles trapezoid - Wikipedia

    en.wikipedia.org/wiki/Isosceles_trapezoid

    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 ...

  7. Icositetragon - Wikipedia

    en.wikipedia.org/wiki/Icositetragon

    Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms. [3] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.

  8. Uniform antiprismatic prism - Wikipedia

    en.wikipedia.org/wiki/Uniform_antiprismatic_prism

    A pentagonal antiprismatic prism or pentagonal antiduoprism is a convex uniform 4-polytope. It is formed as two parallel pentagonal antiprisms connected by cubes and triangular prisms. The symmetry of a pentagonal antiprismatic prism is [10,2 +,2], order 40. It has 20 triangle, 20 square and 4 pentagonal faces. It has 50 edges, and 20 vertices.

  9. Outline of geometry - Wikipedia

    en.wikipedia.org/wiki/Outline_of_geometry

    Absolute geometry; Affine geometry; Algebraic geometry; Analytic geometry; Birational geometry; Complex geometry; Computational geometry; Conformal geometry