3D Unit-Distance Graphs

blue polyhedra

Cube

green polyhedra

Tetrahedron

roll

0.1

pitch

0.2

yaw

0.3

In two dimensions, the Harborth graph has four unit-length edges meeting at each vertex. In other words, it has valency four. In three dimensions, the octahedron has valency four. The icosahedron has valency five. What about valency six?

This Demonstration combines smaller polyhedral graphs to obtain larger unit distance with high valency. This combination method is sometimes called the graph product.

You can vary the roll, pitch, and yaw (in radians) on the graphic.