  The Burling sequence is a sequence of triangle-free graphs of increasing
chromatic number. Each of them is isomorphic to the intersection graph of a set
of axis-parallel boxes in $R^3$. These graphs were also proved to have other
geometrical representations: intersection graphs of line segments in the plane,
and intersection graphs of frames, where a frame is the boundary of an
axis-aligned rectangle in the plane. We call Burling graph every graph that is
an induced subgraph of some graph in the Burling sequence. We give five new
equivalent ways to define Burling graphs. Three of them are geometrical, one is
of a more graph-theoretical flavour and one is more axiomatic.
