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Omni-MATH / An icosahedron is a regular polyhedron with twenty faces, all of which are…

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problem

An icosahedron is a regular polyhedron with twenty faces, all of which are equilateral triangles. If an icosahedron is rotated by θ\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 θ\theta?
Plain-text mathematical notation (without MathML)
An icosahedron is a regular polyhedron with twenty faces, all of which are equilateral triangles. If an icosahedron is rotated by θ 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 θ?
Original LaTeX notation
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 $\theta$?

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Source and history

task_id
50085329-945e-56cd-a5c9-f78df5443759
task_key
test--50085329-945e-56cd-a5c9-f78df5443759
task_revision_id
1
config / split
/ test

Official source

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