Diagonals of a Polyhedron..
A convex polyhedron P has 26 vertices, 60 edges, and 36 faces, 24 of which are triangular and 12 of which are quadrilaterals.
A space diagonal is a line segment connecting two non-adjacent vertices that do not belong to the same face.
How many space diagonals does P have?
The answer is 241.
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1 solution
There are (26C2) possible line segments between vertices of P. 60 of these are edges between adjacent vertices, and 2*12 = 24 are diagonals on one of the quadrilateral faces (note the triangular faces have 0 diagonals).
Thus there are a total of (26C2) – 60 – 24 = 241 space diagonals