Complete Graph K7 Embedded on a 3D Torus

thingiverse

K7 is the complete graph on 7 vertices. You start with 7 vertices, and connect every pair with an edge, leading to 21 edges. It is not a planar graph, meaning it is impossible to draw K7 in the plane without having some edges cross. However, it is possible to embed the graph on a torus and not have any edges intersect. This design demonstrates this idea. This object was designed by my research student, Zachary Ash, at Grand Valley State University. A companion object which demonstrates the embedding when the torus is drawn on the plane, is here: http://www.thingiverse.com/thing:1625128 The printed torus in the photograph was created by Shapeways, for about $20.