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If a regular polygon has all "square corners" (right angles) then it has 4 sides, is a quadrilateral, is a parallelogram and is a square.

If it is NOT a regular polygon and has ONE square corner it is a isosceles right triangle (one 90 degree angle, two 45 degree, two equal side lengths).

A three-dimensional shape would not be called a rectangle or square, but rather a cuboid or cube, a type of polyhedron.

Q: What would a shape be called with some sides the same length and square corners if it is not a quadrilateral?

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You could be like the side elevation of a staircase.

A square or quadrilateral.

When all the vertices of a plane quadrilateral are exactly equal to 90 degrees it is is called a rectangle and, if all its sides are of equal length, that rectangle is called a square. So when a plane quadrilateral has all its vertices exactly equal to 90 degrees, but it does not have all its sides equal in length, it must be a rectangle but not a square.

a trapezoid

Rectangle or a square.

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That is, a quadrilateral with no square corners is not a rectangle or a square. This is because by definition, a rectangle and a square have four square corners, so if a quadrilateral has no square corners, then it cannot be a rectangle or a square.

rectangle

You could be like the side elevation of a staircase.

A square.

There is, unfortunately, no special name.

It is a square or a rhombus

A square or quadrilateral.

When all the vertices of a plane quadrilateral are exactly equal to 90 degrees it is is called a rectangle and, if all its sides are of equal length, that rectangle is called a square. So when a plane quadrilateral has all its vertices exactly equal to 90 degrees, but it does not have all its sides equal in length, it must be a rectangle but not a square.

a trapezoid

Rectangle or a square.

A square is a two-dimensional shape that has four sides (a quadrilateral), where all of the sides are of equal length, and all of the corners form 90 degree angles. A square can be described as an equilateral rectangle, or conversely as an equiangular rhombus.An architectural square surrounded by buildings can be called a quadrangle or courtyard.

A quadrilateral is a four sided geomentric shape. A square is a special quadrilateral where all sides are the same length. A square is also called an equilateral quadrilateral. So for a quadrilateral to not be a square, some of the sides would have to be different lengths, like a rectangle. Specifically to the question: a quadrilateral is not like a square because not all quadrilaterals are squares.