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Euclid’s Elements – Book 1 – Definitions, definition XXII, simply says:
“A quadrilateral figure is one which is bounded by four sides.”
So any four sided shape is a quadrilateral. The shape I use in this piece is a form of a quadrilateral that Euclid describes as a kite. Yes, it’s the shape your thinking of, like the traditional flying kite shape.
In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other rather than adjacent.
The diagonals of a kite are always perpendicular to each other.