The graph named "Fred"

On the campus of the Ohio State University, in front of the math building, there are mathematical designs in bricks that passers-by tread upon. The most intriguing of these designs is the graph named "Fred":

This is a graph consisting of 24 nodes where each node is connected to 3 other nodes.

What is remarkable about "Fred" is that "Fred" cannot be drawn on a torus without lines crossing but "Fred" can be drawn on a möbius strip without lines crossing. Wild stuff!