a circle or a sphere
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The shape that has no vertices and is round is a circle. The circle is the only shape that does not have vertices.
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).