EnumaElish
Science Advisor
Homework Helper
- 2,273
- 123
Is there a 3-D object with 3 faces? What is it called?
Playing Captain Obvious these days? :tongue2: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?A cylinder? Or must the faces be flat..?
A trihedron, of course! :PIs there a 3-D object with 3 faces? What is it called?
Getting the right idea =] No one had stated the shape has to be closed.A tetrahedron with its base removed?
Hello,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?
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.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.
Good thinking. Why wouldn't it? Make the edges thicker = 3 faces.Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
It only has 1 'face' and 1 edge though. And a Möbius strip is 2-dimensional (as a manifold).Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.