How does one show that the sum of the solid angles in a parallelepiped is $4\pi$ steradians? It's easy to see that the sum of angles in a parallelogram is $2\pi$ radians using the definition of parallel lines, but I'm having trouble generalizing this to the $3$ dimensional case.
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Hint: "Tile" $3$-dimensional space with the parallelepiped.
answered Feb 28 '13 at 4:40
