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What is a 3-faced 3-D object?

  1. Jan 13, 2008 #1


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    Is there a 3-D object with 3 faces? What is it called?
  2. jcsd
  3. Jan 13, 2008 #2
    My mind cant comprehend the existence of such a shape :redface:
  4. Jan 13, 2008 #3
    Thats like asking for a 2 sided 2D object.
  5. Jan 13, 2008 #4
    A politician?
  6. Jan 13, 2008 #5


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    A cylinder? Or must the faces be flat..?
  7. Jan 13, 2008 #6


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    No such object exists with flat sides.
  8. Jan 13, 2008 #7
    three lines can only intersect in one point, coincide or be parallel so yes, no such object exists.
  9. Jan 13, 2008 #8

    Gib Z

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    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.
  10. Jan 13, 2008 #9
    A tetrahedron with its base removed?
  11. Jan 13, 2008 #10
    Playing Captain Obvious these days? :tongue2:
  12. Jan 13, 2008 #11


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    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?
  13. Jan 13, 2008 #12
    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.
    Last edited: Jan 13, 2008
  14. Jan 13, 2008 #13

    Ben Niehoff

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    A trihedron, of course! :P
  15. Jan 14, 2008 #14

    Gib Z

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    Getting the right idea =] No one had stated the shape has to be closed.
  16. Jan 16, 2008 #15

    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.
  17. Jan 17, 2008 #16
    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.
  18. Jan 17, 2008 #17


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    Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
  19. Jan 17, 2008 #18


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    Good thinking. Why wouldn't it? Make the edges thicker = 3 faces.

    But obviously no flat surfaced object could have 3 faces. (politicians aside)
  20. Jan 17, 2008 #19
    Are there geometries where such an object could be constructed or is that a silly question to ask?
  21. Jan 18, 2008 #20
    It only has 1 'face' and 1 edge though. And a Möbius strip is 2-dimensional (as a manifold).
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