According to the Euler characteristic, the number of faces, edges and vertices are related by:
V - E + F = 2 for ANY convex polyhedron.
If V = E then F = 2 faces.
Also, E = F requires V = 2 vertices.
No such figure exists.
Any pyramid.
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.
All three dimensional figures have more faces than a one dimensional figure. There are an infinite number of one dimensional points on a three dimensional figure
no numbers have the same number of edges and vertices
pyramid
Any pyramid.
Using the Euler cahracteristic, these two items of information uniquely determine the number of faces for a simply connected polyhedron. That might help you make a three dimensional figure but you will need to be practised to recognise patterns in these numbers.
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.
All three dimensional figures have more faces than a one dimensional figure. There are an infinite number of one dimensional points on a three dimensional figure
no numbers have the same number of edges and vertices
pyramid
There is no limit to the number of vertices that a solid figure can have.
The question is rather confused since a tetracontakaioctagon is a 2-dimensional shape whereas a prism is 3-dimensional. Moreover, [3-dimensional] polyhedra are generally named according to the number of faces that they have and, apart from the tetrahedron, the number of vertices is indeterminate. A pentahedron (5- faces) can have 4 or 5 vertices.
any pyramid
Number of vertices in the plane figure = 4.
A triangular based pyramid has 4 faces and 4 vertices
Yes, a prism has an even number of vertices. A prism is a three-dimensional shape with two parallel and congruent polygonal bases connected by rectangular or parallelogram faces. The number of vertices in a prism is equal to the number of vertices in its bases plus the number of vertices in the lateral faces. Since each base has an equal number of vertices, and the lateral faces have an even number of vertices, the total number of vertices in a prism is always even.