In my future questions, I would like to reference a 16-dimensional shape. Its three-dimensional version is the cuboctahedron, and its four-dimensional version is the 24-cell.
Coordinates of the cuboctahedron: \begin{align*} (\pm 1, \pm 1, 0) \ (\pm 1, 0, \pm 1) \ (0, \pm 1, \pm 1) \end{align*}
Coordinates of the 24-cell: \begin{align*} (\pm 1, \pm 1, 0, 0) \ (\pm 1, 0, \pm 1, 0) \ (0, \pm 1, \pm 1, 0) \ (0, 0, \pm 1, \pm 1) \ (0, 0, \pm 1, 0, \pm 1) \ (\pm 1,0,0, \pm 1) \end{align*}
This 16-dimensional shape has 480 points with coordinates: \begin{align*} (\pm 1, \pm 1, 0, 0, \ldots, 0) \ (\pm 1, 0, \pm 1, 0, \ldots, 0) \ (0, \pm 1, \pm 1, 0, \ldots, 0) \ (0, 0, \pm 1, \pm 1, \ldots, 0) \ \ldots \ (0, 0, \ldots, 0, \pm 1, 0, \pm 1) \ (0, 0, 0, \ldots, 0, \pm 1, \pm 1) \end{align*}
What is the name of this 16-dimensinal shape, and how can I reference it in the future?