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
Solution by Dej Mar)
I'm doing this a totally different way and getting a totally different answer. Tell me which one of us is wrong:
It's easier to count all segments connecting all vertices, obviously: 24 C 2=276. Clearly, I've just counted too many segments. Some of those are edges to the polyhedron--there are 36 edges, so that reduces my number to 240. Finally, you've got all the diagonals of all the octagons to account for--by my calculations, there are 120 of those. (20 diagonals per octagon * 6 octagons.) That leaves me with only 120 segments that pass through the body of the solid.
re: Solution
