Rhombus

A planar quadrilateral in which all four sides are of equal length, called hash ( plural: diamonds) or rhombus (plural: diamonds). While opposite sides are parallel and opposite angles are equal in size.

Designations and maps

In addition to diamond and rhombus sometimes the term is used Karo.

The lozenge is a special type of parallelogram. A special case of the diamond is again the square that, standing on the top, is sometimes also referred to disparagingly called diamond. This has its cause in the fact that the term square sometimes only its edges parallel representation is associated in the reference system. In extreme cases, the tip of representation, it is then considered as another object and thus gets a different name.

Diamond as a symbol and characters

In heraldry hot diamond-shaped elements also Wecke and spindle, which asked for the top square and cube edges.

Diamonds as characters found in Unicode in the block Geometric shapes, such as ◆ (U 25 C6 black diamond " full surface diamond " ), ◇ (U 25 C7 white diamond " hollow diamond " ) and ◊ (U 25 CA lozenge " rhombus ").

The # sign is often mistakenly referred to in connection with telephone and computer keyboards than diamond.

Geometry

A diamond or rhombus is a flat rectangle with four equal sides ( equilateral quadrilateral ).

• It is convex.
• Opposite sides are parallel.
• The two diagonals are symmetry axes.
• The diagonals are perpendicular and bisect each other.
• Opposite angles are equal; adjacent angles are complementary to 180 °.
• Each interior angle is bisected by a diagonal.
• Each diamond has an inscribed circle, but only the right angle ( ie the square of ) a radius.

The rhombus is a kite quadrilateral with pairwise parallel sides. A diamond, for which one calls a right angle, is already a square. To construct a rhombus two determining pieces (such as the side length of a, and one of the two angle ) is necessary.

Occurrence and application

For Stern to close only those diamonds that meet the condition that the central angle, ie the angle at the top, in which one puts them together, is equal to a natural number. They then form an n- pointed star. This does not apply to the three-dimensional case, this can also be anderswinklige diamonds in their head put together, and then produce pyramid-shaped peaks.

• Practical applications: Diamond stars seem neutral, star of trapezoids pointed, ie dynamically when the long half- diagonal is on the outside, otherwise dull. This is used in the decoration being aware.
• The Rhombendach is composed of four diamond-shaped roofs. It allows for a square plan by 45 degrees offset pitched roof ( do not drain the water through the portals).

Rhombendach the Marienkirche (Dortmund )

By its definition, each rhombus for a comprehensive tiling, but only in two main directions ( Platonic tiling ) is suitable. Here the Rautenparkettierung forms (with its special shape, the square lattice, ie an orthogonal grid ) one of the 17 possible symmetry groups of tilings.

• A special feature is the aperiodic ( quasi-crystalline ) Penrose tiling of two diamonds with 36 ° / 144 ° and 72 ° / 108 °.
• Technical applications: The Rhombendach has good Wasserleiteigenschaften, as the water drips on the lower peaks, and just needs a nailing at the upper tip. It is suitable for flat steel molds such as asbestos or sheet metal and wood shingles.
• In the rhombus or diamond-shaped formwork is in the mathematical sense usually not diamond-shaped wooden profiles, but parallelograms ( cross section of the horizontal battens mounted switch, which then also defined a drip edge have ).

Rhombenparketierung with 3D effect ( Kolorierungvariante of the triangular lattice)

Penrose tiling

Rhombohedron, rhombic dodecahedron and Rhombentriakontaeder are polyhedra whose bodies are limited only by diamonds.