# What is a 3-faced 3-D object?

by EnumaElish
Tags: 3faced, object
 Sci Advisor HW Helper P: 2,481 Is there a 3-D object with 3 faces? What is it called?
 P: 555 My mind cant comprehend the existence of such a shape
 P: 116 Thats like asking for a 2 sided 2D object.
 P: 688 What is a 3-faced 3-D object? A politician?
 Sci Advisor P: 1,807 A cylinder? Or must the faces be flat..?
 Mentor P: 17,344 No such object exists with flat sides.
 P: 1,705 three lines can only intersect in one point, coincide or be parallel so yes, no such object exists.
 HW Helper P: 3,348 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.
 P: 352 A tetrahedron with its base removed?
P: 1,520
 Quote by Gib Z 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.
Playing Captain Obvious these days?
HW Helper
P: 2,481
 Quote by Jarle A cylinder? Or must the faces be flat..?
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?
 P: 1,520 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.
P: 1,594
 Quote by EnumaElish Is there a 3-D object with 3 faces? What is it called?
A trihedron, of course! :P
HW Helper
P: 3,348
 Quote by uman A tetrahedron with its base removed?
Getting the right idea =] No one had stated the shape has to be closed.
P: 49
 Quote by EnumaElish 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?
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.
P: 86
 Quote by masnevets 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.
 Sci Advisor HW Helper P: 8,953 Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
P: 389
 Quote by mgb_phys Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
Good thinking. Why wouldn't it? Make the edges thicker = 3 faces.

But obviously no flat surfaced object could have 3 faces. (politicians aside)

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