If you are comparing with a square then you are thinking of 2D shapes not 3D. The answer is yes there are other 2D shapes that tessellate.
You have to look no further than nature to provide an example; the hexagon which is the shape that provides the basis for the honeycomb that bees use!
Another example would be some triangles. For example, two equal right angle triangles will fit together to form a rectangle (which clearly tessellates).
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yes it can, it is quite easy to pick a non tessellate shape and pick another shape(tessellate or not) that when put together make a square and there you go.
No, a square is a 2d shape, although a 3d shape can be made using multiple squares at different angles than 180 or 0 to each other.
Yes. A square is also a parallelogram.
diamond A rhombus is the math name. It's just a slanty square.
Any shape other than a cube.Any shape other than a cube.Any shape other than a cube.Any shape other than a cube.