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30 May, 17:17

What is the Euler characteristic of a polyhedron that has 6 vertices, 12 edges, and 7 faces?

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  1. 30 May, 17:23
    0
    Regardless of the form of the hexahedron, for simply-connected spaces, the Euler Characteristic is 2, giving the formula 2 = V - E + F, where V is the number of vertices, E is the number of edges and F is the number of faces. In this case we have 2 = V - 12 + 6, or

    V = 2 + 12 - 6 = 8.
  2. 30 May, 17:47
    0
    The Euler formula is Vertices-Edges+Faces so lets plug it in.

    6-12+7=

    1 is the answer
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