a shape with 7 vertices
Since the number of sides and vertices is different, it cannot be a 2-dimensional shape. The only 3-dimensional shape with 4 vertices is a tetrahedron and that does not have 6 sides. Consequently, there is no such shape.
Polygon
a cube i guess
A shape with four sides and three vertices does not exist in Euclidean geometry. In Euclidean geometry, a shape must have the same number of sides as vertices. Therefore, a shape with four sides would have four vertices.
A shape with 7 sides.
a shape with 7 vertices
A hexagon.
Since the number of sides and vertices is different, it cannot be a 2-dimensional shape. The only 3-dimensional shape with 4 vertices is a tetrahedron and that does not have 6 sides. Consequently, there is no such shape.
a hexagon
Polygon
Shape has fewer than 6 sides
A shape with four sides has four vertices and a shape with three sides has three vertices, so a shape with four sides has more vertices than a shape with three sides.
a cube i guess
A shape with four sides and three vertices does not exist in Euclidean geometry. In Euclidean geometry, a shape must have the same number of sides as vertices. Therefore, a shape with four sides would have four 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).
A pentagonal pyramid (5 sides and 1 base) has 6 faces, 6 vertices, and 10 edges (5 between the sides and 5 with the base).