There is no limit to the number of sides that a particular shape can have. The Icosahedron has 20 sides.
It would tend to the circle as the number tends to infinity: even a 360-sided polygon (1 degree internal angles) would look a bit like like a pixellated circle.
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A diamond has 4 sides.
A hexagon has six sides.
A Square has 4 sides, the shape you want that has twice as many sides as this is called a Octagon. ( Oct = 8 - as in Octopus ).
Three.
a polygon