          # Rhombus

• rhombus two rhombi
edges and vertices4
schläfli symbol{ } + { }
coxeter diagram   symmetry groupdihedral (d2), , (*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.

• etymology
• characterizations
• basic properties
• diagonals
## For other uses, see Rhombus (disambiguation). Rhombus Two rhombiTypequadrilateral, parallelogram, kiteEdges and vertices4Schläfli symbol{ } + { }Coxeter diagram   Symmetry groupDihedral (D2), , (*22), order 4Area$K={\frac {p\cdot q}{2}}$ (half the product of the diagonals)Dual polygonrectanglePropertiesconvex, 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. Contents 1 Etymology 2 Characterizations 3 Basic properties 4 Diagonals 5 Inradius 6 Area 7 Dual properties 8 Cartesian equation 9 Other properties 9.1 As the faces of a polyhedron 10 See also 11 References 12 External links  