| 11. | Okounkov s construction relies on an earlier result of Askold Khovanskii on semigroups of lattice points.
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| 12. | The 2160 deep holes near the origin are exactly the halves of the norm 4 lattice points.
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| 13. | The noise function then returns the interpolated number based on the values of the surrounding lattice points.
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| 14. | This allows the diffraction experiment to reveal more of the two-dimensional distribution of reciprocal lattice points.
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| 15. | It has a net total of 2 lattice points per unit cell ( ?8 + 1 ).
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| 16. | Generalizing this idea, one might ask about something related to lattice points in three or more dimensions.
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| 17. | Since both rotations mentioned are symmetry operations, A'and B'must both be lattice points.
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| 18. | At these values of \ mathbf { q } the wave from every lattice point is in phase.
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| 19. | A rotation symmetry in dimension 2 or 3 must move a lattice point to a vectors in the figure.
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| 20. | Hence, there are 3 lattice points per unit cell in total and the lattice is non-primitive.
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