Tetrad

The tetrad is an exotic edge with 4 vertices. It appears as the vertex figure of the complex dipentagon and the edge figure of various exotic polyhedroids.

4-edge
The 4-edge is a regular complex edge, which is abstractly equivalent to the tetrad.

Vertex coordinates
A 4-edge with unit circumradius has vertices at the 4th roots of unity.
 * $$1$$
 * $$i$$
 * $$-1$$
 * $$-i$$