Try this beautiful problem from Math Olympiad Hanoi, 2018 based on Cubes and Rectangles.
Find the number of rectangles can be formed by the vertices of a cube.
Geometry
Permutation
Combination
But try the problem first...
Answer: 12.
Math Olympiad Hanoi 2018
Geometry Vol I to IV by Hall and Stevens
First hint
There are 6 squares on 6 faces on the cube.
Second Hint
There are 4 diagonals of the cube that have the same length
and pass through the center of the cube. Every two diagonals intersect at the midpoint and form a rectangle.
Final Step
Then there are 6+ $(\frac{4!}{2!2!})$ =12 rectangles.
Math Olympiad Program... taught by Olympians and researchers
