Complete Graph K7 Embedded in Torus -- Demonstration by aboufade

Last crawled date: 4 years, 2 months ago

From discrete mathematics, K7 is the complete graph with 7 nodes. Each node is connected to all other nodes. K7 is not planar, which means you cannot draw it without having the connections (the edges) cross. However, if you use the 2-dimensional representation of a torus, then you can embed K7 in that representation, and it is planar. This 3D print demonstrates this fact, with the deep ridges being the edges, and their intersection points are the nodes. For more information about this mathematical topic: https://en.wikipedia.org/wiki/Heawood_number
There are two STL's -- one with K_7 engraved on the back, and one without.