# Icosahedron if rotated

**Geometry**Level 5

An icosahedron is a regular polyhedron with twenty faces, all of which are equilateral triangles. If an icosahedron is rotated by \(\theta\) degrees around an axis that passes through two opposite vertices so that it occupies exactly the same region of space as before, what is the smallest possible positive value of \(\theta\)?

- Submit your answer in degrees.