16-cell-color

The 16-cell is a regular 4D polytope, or 4-orthoplex,  which is the 4th dimensional analog to a regular octahedron.   The orthoplex has 8 vertices,  24 edges, and 16 tetrahdral cells, which form the 4D analyagy to  faces in 3D, and 32 triangular faces. There are 4 cells around each edge, and 8 around each vertex.   It is the dual of the 4D cube, or tesseract.

The vertices and edges have been stereographically projected, first onto the circumscribing 4D hypersphere, making the straight edges into portions of great circles, then  into 3 dimensions  from a point on top of the hypersphere. The edges are assumed here to be dimensionless lines, and hence do not change thickness when projected.   In a stereographic projection,straight  lines on the original solid become circular arcs, angles are preserved, but edge length is not. The 24 edges become 6 circles, each composed of 4 edges as circular arcs, which in 4D would all be equal in length.