A cube has 8 vertices. If each vertex is cut off to form a triangle, the new solid will have 3 x 8 = 24 vertices. If each of these vertices is then connected directly to each of the others via a straight line segment, how many of these segments will go through the body of the solid, rather than along its surface?

(In reply to re: Solution by Stephanie)

You are correct Stephanie.  I failed to divide by 2 when calculating the number of connected vertices where the two triangular facets shared only one octagonal face.  I've corrected my earlier post.  Thank you.

Posted by Dej Mar on 2008-02-14 23:10:58