Cross-polytope
= Cross-polytope
{title2=$\operatorname{conv}\{\pm e_1,\ldots,\pm e_n\}$}
{wiki}
The <convex hull> of the positive and negative coordinate <unit vectors>. Its boundary triangulates a <sphere>, and each face contains at most one member of each antipodal pair of coordinate <unit vectors>. This makes its <barycentric subdivision> useful for triangulating <Real projective space>.