  The Babylonian graph B has the positive integers as vertices and connects two
if they define a Pythagorean triple. Triangular subgraphs correspond to Euler
bricks. What are the properties of this graph? Are there tetrahedral subgraphs
corresponding to Euler tesseracts? Is there only one infinite connected
component? Are there two Euler bricks in the graph that are disconnected? Do
the number of edges or triangles in the subgraph generated by the first n
vertices grow like of the order n W(n), where n is the product log? We prove
here some first results like the threshold where B(n) becomes non-planar. In an
appendix, we include handout from a talk on Euler cuboids given in the year
2009.
