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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.
Rhombus (equilateral parallelogram) Lozenge; Rhomboid; Rectangle. square (regular quadrilateral) ... Compound of two great inverted snub icosidodecahedra;
Geometric Shapes; Range: U+25A0..U+25FF (96 code points) Plane: BMP: Scripts: Common: Symbol sets: Control code graphics Geometric shapes: Assigned: 96 code points
The Merkel-Raute [1] (German for "Merkel rhombus"), termed the Merkel diamond [2] or Triangle of Power by English-speaking media, [3] is a hand gesture made by resting one's hands in front of the stomach so that the fingertips meet, with the thumbs and index fingers forming a rough quadrangular shape.
Compound of two great inverted snub icosidodecahedra; Compound of two great retrosnub icosidodecahedra; Compound of two great snub icosidodecahedra; Compound of two icosahedra; Compound of two inverted snub dodecadodecahedra; Compound of two small stellated dodecahedra; Compound of two snub cubes; Compound of two snub dodecadodecahedra
In addition, any two non-intersecting circles may be inverted into congruent circles, using circle of inversion centered at a point on the circle of antisimilitude. The Peaucellier–Lipkin linkage is a mechanical implementation of inversion in a circle. It provides an exact solution to the important problem of converting between linear and ...
The rhombus has a square as a special case, and is a special case of a kite and parallelogram.. In plane Euclidean geometry, a rhombus (pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length.
Additionally, if a convex kite is not a rhombus, there is a circle outside the kite that is tangent to the extensions of the four sides; therefore, every convex kite that is not a rhombus is an ex-tangential quadrilateral. The convex kites that are not rhombi are exactly the quadrilaterals that are both tangential and ex-tangential. [16]