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Each vertex with the obtuse rhombic face angles is shared by 4 cells; each vertex with the acute rhombic face angles is shared by 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron , which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal ...
Let φ be the golden ratio.The 12 points given by (0, ±1, ±φ) and cyclic permutations of these coordinates are the vertices of a regular icosahedron.Its dual regular dodecahedron, whose edges intersect those of the icosahedron at right angles, has as vertices the 8 points (±1, ±1, ±1) together with the 12 points (0, ±φ, ± 1 / φ ) and cyclic permutations of these coordinates.
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The other coordinates can be obtained from vector addition [5] of the 3 direction vectors: e 1 + e 2, e 1 + e 3, e 2 + e 3, and e 1 + e 2 + e 3. The volume V {\displaystyle V} of a rhombohedron, in terms of its side length a {\displaystyle a} and its rhombic acute angle θ {\displaystyle \theta ~} , is a simplification of the volume of a ...
The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (±1, ±1, ±1) and (0, 1 + h, 1 − h 2) with parameter h = 1. These coordinates illustrate that a rhombic dodecahedron can be seen as a cube with six square pyramids attached to each face, allowing them to fit together into a ...
Bootstrap Studio is a proprietary web design and development application. It offers a large number of components for building responsive pages including headers, footers, galleries and slideshows along with basic elements, such as spans and divs. [1] The program can be used for building websites [2] and prototypes. [3]
The rhombus in this set has the same size as the blue rhombus in the traditional set. The dart and the 30°–60°–90° triangle have the same area, while the kite and the hexagon are twice that area. Like the traditional set, all the angles are multiples of 30°.
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]