Quadrilateral - More Quadrilaterals

More Quadrilaterals

• An equilic quadrilateral has two opposite equal sides that, when extended, meet at 60°.
• A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length.
• A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square.
• A geometric chevron (dart or arrowhead) is a concave quadrilateral with bilateral symmetry like a kite, but one interior angle is reflex.
• A self-intersecting quadrilateral is called variously a cross-quadrilateral, crossed quadrilateral, butterfly quadrilateral or bow-tie quadrilateral. A special case of crossed quadrilaterals are the antiparallelograms, crossed quadrilaterals in which (like a parallelogram) each pair of nonadjacent sides has equal length. The diagonals of a crossed or concave quadrilateral do not intersect inside the shape.
• A non-planar quadrilateral is called a skew quadrilateral. Formulas to compute its dihedral angles from the edge lengths and the angle between two adjacent edges were derived for work on the properties of molecules such as cyclobutane that contain a "puckered" ring of four atoms. See skew polygon for more. Historically the term gauche quadrilateral was also used to mean a skew quadrilateral. A skew quadrilateral together with its diagonals form a (possibly non-regular) tetrahedron, and conversely every skew quadrilateral comes from a tetrahedron where a pair of opposite edges is removed.