Question

How come a three-dimensional figure with a curved surface is not a polyhedron?

Answer 1

Polyhedron, by definition, is formed by intersecting planes, so each part of its surface is either a vertex or an edge, or a flat piece of a plane.

Explanation:

The definition of polyhedron implies that each side is a piece of a flat surface.

Answer 2

Each face of a polyhedron is a polygon, which by definition is a two dimensional closed shape, bounded by straight lines.

Therefore a circle is not a polygon,

In the same way, the faces of a polyhedron (a three-dimensional figure) have to be planes with straight edges,

A cylinder and a cone are therefore not considered to be polyhedra because they have curved surfaces.