The rhombus is named after an ancient spinning toy
Diamond, lozenge, calisson: the four-sided shape with equal edges has a menu of names, one of them a French sweet. The word rhombus itself comes from a Greek term for something that spins, such as a bullroarer, and Euclid and Archimedes both used it.
A rhombus is a quadrilateral whose four sides are all the same length. It never crosses itself, and it counts as a special case of both a parallelogram and a kite. Give it right angles and it becomes a square; otherwise it has one pair of opposite sharp angles and one pair of opposite blunt ones.
Its names have colourful histories. Greek rhombos meant a spinning object, such as a bullroarer or an early form of the button whirligig. Archimedes spoke of a solid rhombus for a bicone, two cones joined at their bases, and a flat rhombus is a slice through such a shape. Diamond comes from the outline of an octahedral gemstone, and the playing-card suit took the name, though in French it was carreaux, squares. Lozenge has an uncertain origin, perhaps almond pastries or tombstones, and often refers specifically to a rhombus with a 45 degree angle. A calisson is a rhombus-shaped French confection.
Many conditions pick out a rhombus. A parallelogram qualifies if a diagonal splits one of its angles in half, if two neighbouring sides are equal, or if its diagonals meet at right angles. Any quadrilateral whose diagonals are perpendicular and bisect each other is also one. Because each diagonal is a mirror line, opposite angles are equal and the diagonals cross at 90 degrees.
It inherits every parallelogram property: opposite sides run parallel, neighbouring angles add to a straight angle, and the parallelogram law applies, so four times the square of a side matches the squared lengths of both diagonals added together. A shape that is both kite and parallelogram must be a rhombus, and every rhombus can hold a circle touching all four sides. Among polyiamonds, shapes glued together from triangles with equal sides, the name diamond is reserved for the rhombus whose sharp corners measure 60 degrees.
Source: Rhombus
