How shapes fit together...

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material composition.
Mathematician and statistician David George Kendall defined shape this way.

Shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an object.

Own photos used.