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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.
A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.
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 ...
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]
In geometry, a bicone or dicone (from Latin: bi-, and Greek: di-, both meaning "two") is the three-dimensional surface of revolution of a rhombus around one of its axes of symmetry. Equivalently, a bicone is the surface created by joining two congruent, right, circular cones at their bases.
The definition of lozenge is not strictly fixed, and the word is sometimes used simply as a synonym (from Old French losenge) for rhombus. Most often, though, lozenge refers to a thin rhombus—a rhombus with two acute and two obtuse angles, especially one with acute angles of 45°. [ 2 ]
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.
In geometry, the rhombille tiling, [1] also known as tumbling blocks, [2] reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets ...
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