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A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).
When more than one type of rhombus is allowed, additional tilings are possible, including some that are topologically equivalent to the rhombille tiling but with lower symmetry. Tilings combinatorially equivalent to the rhombille tiling can also be realized by parallelograms, and interpreted as axonometric projections of three dimensional cubic ...
If it also has exactly two lines of reflectional symmetry then it must be a rhombus or an oblong (a non-square rectangle). If it has four lines of reflectional symmetry, it is a square. The perimeter of a parallelogram is 2(a + b) where a and b are the lengths of adjacent sides.
Rhombus; Square (regular quadrilateral) Tangential quadrilateral; Trapezoid. Isosceles trapezoid; Trapezus; Pentagon – 5 sides; Hexagon – 6 sides Lemoine hexagon; Heptagon – 7 sides; Octagon – 8 sides; Nonagon – 9 sides; Decagon – 10 sides; Hendecagon – 11 sides; Dodecagon – 12 sides; Tridecagon – 13 sides; Tetradecagon – 14 ...
In geometry, a rhombohedron (also called a rhombic hexahedron [1] [2] or, inaccurately, a rhomboid [a]) is a special case of a parallelepiped in which all six faces are congruent rhombi. [3]
A convex quadrilateral is equidiagonal if and only if its Varignon parallelogram, the parallelogram formed by the midpoints of its sides, is a rhombus.An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular.
All side lengths are equal, but the ratio of the length of sides to the short diagonal in the thin rhombus equals : , as does the ratio of the sides of to the long diagonal of the thick rhombus. As with the kite and dart tiling, the areas of the two rhombi are in the golden ratio to each other.
A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.