16-cell, stereographic projection

The 16-cell is a 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 have been stereographically projected here  into 3 dimensions and connected with edges which are also stereographically projected into 3D from 4D (the edges are assumed to be dimensionless lines, and hence do not change thickness when projected).   In a stereographic projection, the straight edges in 4D are first projected onto the circumscribing 4D hypersphere, so the edges become circular arcs. In the projection, angles are preserved, but 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.