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Sep 25, 2011 at 19:40 comment added Noam D. Elkies You're welcome. Of course I in turned committed a typo: the last factor should be $x_0^3 + 8 x_1^3$, not $x_0^3 + 8 x_0^3$...
Sep 25, 2011 at 17:37 history edited JME CC BY-SA 3.0
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Sep 25, 2011 at 17:35 comment added Noam D. Elkies Wait, $x_0^8 + x_1^8 = 0$ gives a regular octagon, not an octahedron (which has six vertices, not eight). If you want 8 points with octahedral symmetry, you're looking for vertices of a cube, e.g. the roots of $x_0 x_1 (x_0^3-x_1^3) (x_0^3 + 8 x_0^3)$.
Sep 25, 2011 at 17:03 history edited JME CC BY-SA 3.0
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Sep 25, 2011 at 16:34 history edited JME CC BY-SA 3.0
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Sep 25, 2011 at 16:06 history answered JME CC BY-SA 3.0