a triangle
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Triangle
That's impossible, because if a shape has sides, then it means it has corners, and vice versa.
A cylinder could fit the given description
There is no such shape. If it has two sides meeting, it also has to have a corner. A triangle has three sides and three corners, and a square has four sides and four corners. There is nothing in between.
the vertices are the corners to the shape, so you count the corners to whatever shape.