In geometry, an antiparallelogram is a type of self-crossing quadrilateral. Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general parallel. Instead, each pair of sides is antiparallel with respect to the other, with sides in the longer pair crossing each other as in a scissors mechanism. Whereas a parallelogram's opposite angles are equal and oriented the same way, an antiparallelogram's are equal but oppositely oriented. Antiparallelograms are also called contraparallelograms[1] or crossed parallelograms.[2]
Antiparallelograms occur as the vertex figures of certain nonconvex uniform polyhedra. In the theory of four-bar linkages, the linkages with the form of an antiparallelogram are also called butterfly linkages or bow-tie linkages, and are used in the design of non-circular gears. In celestial mechanics, they occur in certain families of solutions to the 4-body problem.
Every antiparallelogram has an axis of symmetry, with all four vertices on a circle. It can be formed from an isosceles trapezoid by adding the two diagonals and removing two parallel sides. The signed area of every antiparallelogram is zero.
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In geometry, an antiparallelogram is a type of self-crossing quadrilateral. Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length...
which one pair of nonadjacent sides is parallel (like a trapezoid). Antiparallelogram: a crossed quadrilateral in which each pair of nonadjacent sides have...
quadrilaterals are most common, including: crossed parallelogram or antiparallelogram, a crossed quadrilateral with alternate edges of equal length. crossed...
Antiparallel (electronics), the polarity of devices run in parallel Antiparallelogram This disambiguation page lists articles associated with the title...
(therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite...
Sylvester in the journal Nature. Like Hart's inversor, it is based on an antiparallelogram but the rather than placing the fixed, input and output points on...
faces are parallelograms. Fundamental parallelogram (disambiguation) Antiparallelogram Levi-Civita parallelogramoid "CIMT - Page no longer available at Plymouth...
360°, e.g. 720° for a pentagram and 0° for an angular "eight" or antiparallelogram, where d is the density or turning number of the polygon. In this...
Anthology or Collection Contents Publication Date 21st Century Dead Antiparallelogram Jul 2012 An Apple for a Creature Callie Meet Happy Aug 2012 Life Inside...
extreme configurations of the second animation, which has an equatorial antiparallelogram. It is also possible to think of the Bricard octahedron as a mechanical...
20 hexagons), 120 edges and 60 vertices. Its vertex figure is an antiparallelogram. A rhombicosahedron shares its vertex arrangement with the uniform...
have a circumcircle. Any square, rectangle, isosceles trapezoid, or antiparallelogram is cyclic. A kite is cyclic if and only if it has two right angles...
to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces. Maeder, Roman. "39: small rhombidodecahedron". MathConsult...
to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces. Each face has two angles of arccos ( 5 8 + 1 8 5 ) ≈ 25.242...
and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram. This polyhedron shares the vertex arrangement with the stellated...
hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar triangles. Each antiparallelogram has two angles of arccos ( 1 4 +...
{5}})\approx 81.816\,127\,508\,183^{\circ }} . The diagonals of each antiparallelogram intersect at an angle of arccos ( 5 12 − 1 60 5 ) ≈ 67.703 547 926...
{5}})\approx 129.657\,475\,656\,13^{\circ }} . The diagonals of each antiparallelogram intersect at an angle of arccos ( 1 12 + 19 60 5 ) ≈ 37.681 445...
to the great deltoidal hexecontahedron. Its faces are antiparallelograms. Each antiparallelogram has two angles of arccos ( 1 2 + 1 5 5 ) ≈ 18.699 407...
does. The dual of the crossed pentagonal cuploid has 5 kite and 5 antiparallelogram faces, and may be called the crossed pentagonal keratinoid after Inchbald...
{1}{6}})\approx 99.594\,068\,226\,86^{\circ }} . The diagonals of each antiparallelogram intersect at an angle of arccos ( 1 8 + 7 5 24 ) ≈ 38.996 309 663...
has 11 faces. The dual of the pentagrammic cuploid has 5 kite and 5 antiparallelogram faces, and has been called the pentagrammic keratinoid by Inchbald...
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