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 and edges have been stereographically projected here into 3 dimensions (the edges are assumed to have thickness, and hence become thicker when projected stereographically). In a stereographic projection, the straight lines are projected first onto the circumsctibing hypersphere, becoming circular arcs, then projected into 3-space from a point on top of the hypersphere. In this projection, angles are preserved, but length is not, and circles remain circles. The 24 edges become 6 circles, each composed of 4 edges as circular arcs, which in 4D would all be equal in length.