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By using the parallelogram law (see the basic properties of the general rhombus): [5] The edge length of the golden rhombus in terms of the diagonal length d {\displaystyle d} is: a = 1 2 d 2 + ( φ d ) 2 = 1 2 1 + φ 2 d = 2 + φ 2 d = 1 4 10 + 2 5 d ≈ 0.95106 d .
5.2 The Parthenon. 5.3 Modern art. ... or ratios of Fibonacci numbers. The formula ... A golden rhombus is a rhombus whose diagonals are in proportion to the golden ...
The rhombus is often called a "diamond", after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (which some authors call a calisson after the French sweet [1] —also see Polyiamond), and the latter sometimes ...
where φ = 1 + √ 5 / 2 is the golden ratio. Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √ φ 6 +2 = √ 8φ+7 for edge length 2.
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 ...
Penrose's first tiling uses pentagons and three other shapes: a five-pointed "star" (a pentagram), a "boat" (roughly 3/5 of a star) and a "diamond" (a thin rhombus). [28] To ensure that all tilings are non-periodic, there are matching rules that specify how tiles may meet each other, and there are three different types of matching rule for the ...
This is a special case of the n-gon interior angle sum formula: S = (n − 2) × 180° (here, n=4). [ 2 ] All non-self-crossing quadrilaterals tile the plane , by repeated rotation around the midpoints of their edges.
This formula generalizes Heron's formula for triangles and Brahmagupta's formula for cyclic quadrilaterals. [37] Either diagonal of a rhombus divides it into two congruent isosceles triangles. Similarly, one of the two diagonals of a kite divides it into two isosceles triangles, which are not congruent except when the kite is a rhombus. [38]