[4][5] The Tutte 12-cage is a cubic Hamiltonian graph and can be defined by the LCF notation [17, 27, –13, –59, –35, 35, –11, 13, –53, 53, –27, 21, 57, 11, –21, –57, 59, –17]7.

[6] There are, up to isomorphism, precisely two generalized hexagons of order (2,2) as proved by Cohen and Tits.

They are the split Cayley hexagon H(2) and its point-line dual.

Clearly both of them have the same incidence graph, which is in fact isomorphic to the Tutte 12-cage.

[1] The Balaban 11-cage can be constructed by excision from the Tutte 12-cage by removing a small subtree and suppressing the resulting vertices of degree two.