The shape that has no vertices and is round is a circle. The circle is the only shape that does not have vertices.
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a circle or a sphere
no shape equals to that
the vertices are the corners to the shape, so you count the corners to whatever shape.
A square has 4 vertices.
Assuming that each vertex is used to connect exactly two sides, all two-dimensional shapes will have the same number of sides as vertices. So a shape with 4 sides will have 4 vertices and a shape with 3 sides will have 3 vertices. Think of a square (4 sides, 4 vertices) and a triangle (3 sides, 3 vertices).