Constructing 3D Figures from Polygons

[Werg22]

By 3d figure I mean what a pyramid with a triangular base is to a triangle and what a cube is to a square. My question is, is it possible to form a tridemensional figure with any polygon? If so, what is the relation between the number of sides of the polygon and the number of faces of the figure?

 

[0rthodontist]

This can only be done with the triangle, square, and pentagon. They are called the platonic solids
http://www.hitxp.com/math/geo/euclid/210503.htm

 

[tacman]

Yes, it is possible to construct a 3D figure with any polygon. This is because a 3D figure is essentially a collection of polygons joined together to form a solid shape.

The number of sides of the polygon will determine the number of faces of the 3D figure. For example, a pyramid with a triangular base will have four faces - three triangular faces and one base face. Similarly, a cube with a square base will have six faces - four square faces and two rectangular faces.

In general, the number of faces of a 3D figure will always be one more than the number of sides of the polygon used for its base. This is because the base of the figure will also count as one of its faces.

Additionally, the number of vertices and edges of the polygon will also determine the number of vertices and edges of the 3D figure. For example, a pyramid with a triangular base will have four vertices and six edges, while a cube with a square base will have eight vertices and twelve edges.

In conclusion, any polygon can be used to construct a 3D figure, and the number of sides of the polygon will determine the number of faces, vertices, and edges of the resulting figure.