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Quadrilateral
Six names that you can call a square are rhombus, square, rectangle, kite, trapezoid, or parallelogram. All of these shapes have four corners and are known as quadrilaterals.
A trapezium. A trapezium. A trapezium. A trapezium.
A square is also a rectangle, a rhombus, a parallelogram, and a quadrilateral.
You could call the vertex, the apex, the tip, or the point of the cone.