Cross Polytope

A regular Polytope in $n$-D (generally assumed to satisfy $n\geq 5$) corresponding to the Convex Hull of the points formed by permuting the coordinates ($\pm 1$, 0, 0, ..., 0). It is denoted $\beta_n$ and has Schläfli Symbol $\{3^{n-2}, 4\}$. In 3-D, the cross polytope is the Octahedron.

See also Measure Polytope, Simplex