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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]
In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics , where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.
For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse, acute, scalene, etc. while quadrilaterals can be rectangles, rhombi, trapezoids, squares, etc.
Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case.
A Saccheri quadrilateral is a quadrilateral which has two sides of equal length, both perpendicular to a side called the base. The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure. The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, and right angles if the ...
Classification of quadrilaterals by their symmetry subgroups. [11] The 8-fold symmetry of the square is labeled as r8, at the top of the image. The "gyrational square" below it corresponds to the subgroup of four orientation-preserving symmetries of a square, using rotations but not reflections. The square is the most symmetrical of the ...
Quadrilaterals can be classified hierarchically, meaning that some classes of quadrilaterals include other classes, or partitionally, meaning that each quadrilateral is in only one class. Classified hierarchically, kites include the rhombi (quadrilaterals with four equal sides) and squares .
Broken down, 3 6; 3 6 (both of different transitivity class), or (3 6) 2, tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided polygons (triangles). With a final vertex 3 4 .6, 4 more contiguous equilateral triangles and a single regular hexagon.