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What is the smallest number of non-overlapping trihedral angles that can divide space?

#
Let $O$ be a point inside the tetrahedron $A B C D$. Then the four trihedral angles $O A B C, O A B D, O A C D$, and $O B C D$ with the common vertex $O$ satisfy the condition of the problem. It is clear that space cannot be divided into two or three non-intersecting trihedral angles.

## Answer

Into four.