# Problem #1157

 1157 Let $S$ be the set of all points with coordinates $(x,y,z)$, where $x, y,$ and $z$ are each chosen from the set $\{ 0, 1, 2\}$. How many equilateral triangles have all their vertices in $S$? $\mathrm {(A) } 72 \qquad \mathrm {(B) } 76 \qquad \mathrm {(C) } 80 \qquad \mathrm {(D) } 84 \qquad \mathrm {(E) } 88$ This problem is copyrighted by the American Mathematics Competitions.
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