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I want to implement the icosahedral pointgroup. For that I need all angles of the lines between two opposite vertices, between the midpoints of two opposite faces and between the midpoints of two opposite edges.

The more I try to calculate this I get more confused. Maybe you know a good site where this is explained.


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Each of your requests is for the angle between two points, but it takes three points to determine an angle. If you mean opposite as opposite the center, the angle with respect to the center is $180^{\circ}$ Many angle calculations are given here

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