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That is the property of thermoplastics. If they could not be formed into different shapes many many times then nobody would bother to make them.
There is no defining characteristic for the set. Provided they meet certain conditions, there is an infinite number of possibilities. Put the arrow of time in reverse: Take a parallelogram. Cut it up into 7 shapes. What set of shapes do you end up with? Obviously these 7 shapes can be combined to form a parallelogram. Now try different cuts. Then different parallelograms.
If they are the same shapes but differ only in size, then they are SIMILAR shapes. Otherwise, they are simply different shapes.
Crystals form in the shapes of hexagons or six-sided prisms.
Polygonal (2-d) shapes get their (not there) names from the number of sides; polyhedra (3-d) shapes get their names from the number of faces.The names of other shapes: circles, ellipses, torus, cardioid etc have different origins.