Rhombus

  • rhombus
    rhombus.svg
    two rhombi
    typequadrilateral, parallelogram, kite
    edges and vertices4
    schläfli symbol{ } + { }
    coxeter diagramcdel node 1.pngcdel sum.pngcdel node 1.png
    symmetry groupdihedral (d2), [2], (*22), order 4
    area (half the product of the diagonals)
    dual polygonrectangle
    propertiesconvex, isotoxal
    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 (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. the rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (see polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle.

    every rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. a rhombus with right angles is a square.[1][2]

  • etymology
  • characterizations
  • basic properties
  • diagonals
  • inradius
  • area
  • dual properties
  • cartesian equation
  • other properties
  • see also
  • references
  • external links

Rhombus
Rhombus.svg
Two rhombi
Typequadrilateral, parallelogram, kite
Edges and vertices4
Schläfli symbol{ } + { }
Coxeter diagramCDel node 1.pngCDel sum.pngCDel node 1.png
Symmetry groupDihedral (D2), [2], (*22), order 4
Area (half the product of the diagonals)
Dual polygonrectangle
Propertiesconvex, isotoxal
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 (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle.

Every rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. A rhombus with right angles is a square.[1][2]