Projections of the 16-Cell

Rotate a four-dimensional regular cross polytope (or 16-cell, Schlaefli symbol {3,3,4}) and project it into three-dimensional graphics. The rotation is the composite of rotations in the

wx

,

wy

, and

wz

planes, in that order. Opposite tetrahedra (3-cells) of the cross polytope are colored with similar colors. Play with the opacity to see how the cross polytope is bounded by 16 tetrahedra.