Results 1 to 3 of 3
Like Tree2Thanks
  • 2 Post By awkward

Math Help - convex polyhedron

  1. #1
    Member Veronica1999's Avatar
    Joined
    Jan 2010
    From
    Jupimar
    Posts
    160

    convex polyhedron

    A convex polyhedron Q has vertices V1, V2, ..., Vn, and 100 edges. The poly-
    hedron is cut by planes
    P1, P2, ...., Pn in such a way that plane Pk cuts only
    those edges that meet at vertex
    Vk. In addition, no two planes intersect inside
    or on
    Q. The cuts produce n pyramids and a new polyhedron R. How many
    edges does
    R have?




    I'm not fully understanding the problem...
    I've been working hard on this question so any help would be appreciated.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: convex polyhedron

    Let's say k_i edges meet at vertex i. Then cutting the polyhedron at that vertex adds k_i new edges to the new polyhedron, so the total number of new edges is \sum_{i=1}^n k_i, for a total of 100 + \sum_{i=1}^n k_i vertices in R.

    But in the original polyhedron Q, each edge connects two vertices; so \sum_{i=1}^n k_i = 200, hence R has 300 edges.
    Thanks from Veronica1999 and mash
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Veronica1999's Avatar
    Joined
    Jan 2010
    From
    Jupimar
    Posts
    160

    Re: convex polyhedron

    Thanks!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The union of two convex sets is not convex
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: January 30th 2010, 03:23 PM
  2. Convex polyhedron
    Posted in the Geometry Forum
    Replies: 0
    Last Post: March 15th 2009, 02:59 AM
  3. Vertices in polyhedron
    Posted in the Geometry Forum
    Replies: 0
    Last Post: February 17th 2009, 03:09 AM
  4. edges of Polyhedron
    Posted in the Algebra Forum
    Replies: 0
    Last Post: November 18th 2008, 07:59 PM
  5. Polyhedron
    Posted in the Geometry Forum
    Replies: 2
    Last Post: August 29th 2008, 04:42 AM

Search Tags


/mathhelpforum @mathhelpforum