There is an infinite number of 3 dimensional objects with 3 faces, just as there are an infinite number 2 dimensional objects with 2 sides.
Good answer; but I was asking about flat surfaces. I understand that no such object exists. Is there a theorem about the min. number of flat surfaces that a 3-D object must have?
I think it's best we first clarify what a closed 3 dimensional object is for our purposes. I would say that a simple closed 3 dimensional object is a collection of planar surfaces with properties among which is that a surface in that collection connects to at least as many surfaces as it has vertices. The simplest planar figure is the triangle; since it has 3 sides, it is not possible to meet the said property with only 3 planar faces, hence there is no such 3 dimensional object.
Hello, What you are thinking of is a 3 dimensional (convex) polytope. I assume you mean codimension 1 faces (i.e. 2 dimensional faces). Technically, edges and vertices are also called faces. In this case, the minimum number of faces is 4 (a tetrahedron). In general, an n dimensional polytope needs to have at least n+1 facets.
Darn, I was going to say that. Furthermore, when you consider the convex hull of this polytope, the convex hull can extend in two dimensions; but there needs to be at least one point above the plane of the other points in order to achieve what you desire. Otherwise it's simply a 2-dimensional face.
Good thinking. Why wouldn't it? Make the edges thicker = 3 faces. But obviously no flat surfaced object could have 3 faces. (politicians aside)