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A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a ...
The only equable rectangles with integer sides are the 4 × 4 square and the 3 × 6 rectangle. [4] An integer rectangle is a special type of polyomino, and more generally there exist polyominoes with equal area and perimeter for any even integer area greater than or equal to 16. For smaller areas, the perimeter of a polyomino must exceed its area.
Another way, in common with parallelograms, is to consider two adjacent sides as vectors, forming a bivector, so the area is the magnitude of the bivector (the magnitude of the vector product of the two vectors), which is the determinant of the two vectors' Cartesian coordinates: K = x 1 y 2 – x 2 y 1. [11]
A quadrilateral is a square if and only if it is both a rhombus and a rectangle (i.e., four equal sides and four equal angles). Oblong: longer than wide, or wider than long (i.e., a rectangle that is not a square). [5] Kite: two pairs of adjacent sides are of equal length.
Pentagram - star polygon with 5 sides; Hexagram – star polygon with 6 sides Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides; Hendecagram - star polygon with 11 sides; Dodecagram - star ...
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals [4] (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 angles are equal.
The sum of the squared distances from the vertices of a regular n-gon to any point on its circumcircle equals 2nR 2 where R is the circumradius. [4]: p. 73 The sum of the squared distances from the midpoints of the sides of a regular n-gon to any point on the circumcircle is 2nR 2 − 1 / 4 ns 2, where s is the side length and R is the ...
A quadrilateral is equidiagonal if and only if [5]: p.19, [4]: Cor.4 =. This is a direct consequence of the fact that the area of a convex quadrilateral is twice the area of its Varignon parallelogram and that the diagonals in this parallelogram are the bimedians of the quadrilateral.