A generalized hexagon is a generalized polygon of order 6.
is more commonly known as the Heawood graph, but
is also the 
-cage graph, the cubic
vertex-transitive graph Ct15, the cubic symmetric
graph 
,
the 69-Haar graph, and is an incidence graph of a 2-
design.
is the 
-cage graph, 4137-Haar graph,
and is an incidence graph of a 2-
design.
is the Bouwer graph 
, line graph of the Heawood graph, and is a distance-regular
graph with intersection array 
,
is the line graph of the 
-cage, is also known as the flag graph of 
(DistanceRegular.org), and is a distance-regular
graph with intersection array 
.
is the line graph of the 
-cage, is also known as the flag graph of 
(DistanceRegular.org), and is the distance-regular
graph with intersection array 
.
The generalized hexagons 
are line graphs of the
generalized hexagons 
.
The following table summarizes some generalized hexagons.
| graph |  | other names | incidence | graph spectrum |
| GH(1, 2) | 14 | Heawood graph |  |  |
| GH(1, 3) | 26 | (4, 6)-cage
graph, incidence graph of  |  |  |
| GH(1, 4) | 42 | (5, 6)-cage graph |  |  |
| GH(1, 5) | 62 | (6, 6)-cage graph |  |  |
| GH(1, 7) | 114 | (8, 6)-cage graph |  |  |
| GH(1, 8) | 146 | (9, 6)-cage graph |  |  |
| GH(1, 9) | 182 | (10, 6)-cage graph |  |  |
| GH(2, 1) | 21 | (2,3,7)-Bouwer
graph, flag graph of  |  | |
| GH(2, 8) | 819 |  | ||
| GH(3, 1) | 52 |  | ||
| GH(4, 1) | 105 |  | ||
| GH(5, 1) | 186 |  | ||
| GH(7, 1) | 456 |  | ||
| GH(8, 1) | 657 |  | ||
| GH(8, 2) | 2457 |  |
."
." 
and its Dual."