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The rhombic Penrose tiling contains two types of rhombus, a thin rhombus with angles of and , and a thick rhombus with angles of and . All side lengths are equal, but the ratio of the length of sides to the short diagonal in the thin rhombus equals 1 : φ {\displaystyle 1\mathbin {:} \varphi } , as does the ...
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 ...
Therefore, it has the same number of squares as five cubes. Two clusters of faces of the bilunabirotunda, the lunes (each lune featuring two triangles adjacent to opposite sides of one square), can be aligned with a congruent patch of faces on the rhombicosidodecahedron. If two bilunabirotundae are aligned this way on opposite sides of the ...
The golden rhombus. In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: [1] = = + Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle. [1]
Another area formula, for two sides B and C and angle θ, is K = B ⋅ C ⋅ sin θ . {\displaystyle K=B\cdot C\cdot \sin \theta .\,} Provided that the parallelogram is not a rhombus, the area can be expressed using sides B and C and angle γ {\displaystyle \gamma } at the intersection of the diagonals: [ 9 ]
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
It consists of copies of a single cell, the rhombic dodecahedron.All faces are rhombi, with diagonals in the ratio 1: √ 2.Three cells meet at each edge. The honeycomb is thus cell-transitive, face-transitive, and edge-transitive; but it is not vertex-transitive, as it has two kinds of vertex.
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]