Q: What shape has six sides and six vertices?

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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.

There is no such shape.

A pentagon has five sides and five vertices

It is a shape with six straight sides (and six vertices). That is all. So it could look like: |\..../| |..\/..| |......| |../\.| |/...\| Of course, it need not be symmetrical.

A geometric shape with 4 sides and 4 vertices is a 4-sided figure, a quadrilateral.

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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 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.

Six sides and six vertices.

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).

There can be no such shape. A hexagon is a 2-dimensional shape and so has only one face, six sides and 6 vertices.

A shape with 7 sides.

a shape with 7 vertices

The number of vertices does not determine the number of faces. If the shape with 6 vertices was a quadrilateral based bipyramid, it would have 8 faces. A hexagonal based pyramid has 7 vertices and 7 faces. So more vertices does not necessarily imply more faces.

A hexagon has 6 sides and 6 vertices.

Yes. Two triangle touching corner-to-corner. There would be six sides, but only 5 vertices because one vertex is shared.

Six sides and six vertices.