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Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...
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]
The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 arctan( 1 / φ ) = arctan(2), or approximately 63.43°. A rhombus so obtained is called a golden rhombus.
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 ...
Rectangle – A parallelogram with four angles of equal size (right angles).; Rhombus – A parallelogram with four sides of equal length. Any parallelogram that is neither a rectangle nor a rhombus was traditionally called a rhomboid but this term is not used in modern mathematics.
The Bilinski dodecahedron is formed by gluing together twelve congruent golden rhombi.These are rhombi whose diagonals are in the golden ratio: = + The graph of the resulting polyhedron is isomorphic to the graph of the rhombic dodecahedron, but the faces are oriented differently: one pair of opposite rhombi has their long and short diagonals reversed, relatively to the orientation of the ...
The rhombic dodecahedron is a polyhedron with twelve rhombuses, each of which long face-diagonal length is exactly times the short face-diagonal length [1] and the acute angle measurement is (/). Its dihedral angle between two rhombi is 120°. [2]
Every golden rhombic face has a face center, a vertex, and two edge centers of the original dodecahedron, with the edge centers forming the short diagonal. Each edge center is connected to two vertices and two face centers. Each face center is connected to five edge centers, and each vertex is connected to three edge centers.