The illustration on Wolfram's page claims to present a uniquely colorable, triangle-free graph. However, this seems to be blatantly false: the graph has a symmetry with respect to a reflection through the horizontal axis, and we can use this symmetry to construct a new colouring not isomorphic to the original one.

Am I missing something obvious here, or is the illustration simply wrong? If it's the latter, what is a simple example of a triangle-free, uniquely 3-colourable graph?