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To make a cube, I can use 6 4-sided-squares (of course they're 4 sided)

To make a pyramid (3 sided), I can use 4 3-sided-triangles

I can do this with pentagon as well (i don't know what the shape is called)

Eventually I can't do this as the sides of the shape increase because the remaining angle.

... after some thinking I realized I can only do this with 3 equilateral shapes.

3 sided

4 sided

and 5 sided

Once I get to the hexagon ... well

Now here's an even more interesting question: Are there any others shapes convex or concave equilateral or not that can be used to create a 3D shape? (where the base shapes remains the same)

If so how can one determine if a shape is capable of doing this?