The relative energies of the ground state isomers of 1,6-diphenyl-1,3,5-hexatriene (DPH) in benzene are determined from the temperature dependence of the equilibrium isomer composition obtained with the use of diphenyl diselenide as isomerization catalyst. In the triplet state, DPH exists as an equilibrium mixture of all-trans (ttt), trans,cis,trans (tct), cis,trans,trans (ctt), and cis,cis,trans (cct) isomers. Under degassed conditions, photoisomerization of the triplets is primarily bimolecular, involving a quantum chain process. Oxygen eliminates the quantum chain process by efficient deactivation of DPH triplets thereby revealing the triplet state isomeric composition. The temperature dependencies of the fluorenone-sensitized photoisomerization quantum yields and photostationary states for DPH in air-saturated benzene provide two independent measures of the temperature dependence of the equilibrium contribution of the isomeric triplets. They reveal the relative energies of the DPH triplet isomers. Together with the known 34 kcal/mol triplet energy of ttt-DPH, these results define points on the potential energy surfaces of the ground and triplet states corresponding to the equilibrium geometries of the four observed DPH isomers. At these geometries the two surfaces roughly parallel each other. Complete equilibration of isomeric triplets within 100 ns requires that the energies of triplet biradical transition states be no higher than 40.3 kcal/mol. Estimated radical stabilization energies give 40.2 and 41.6 kcal/mol for the energies of biradical transition states for central and terminal bond isomerization, respectively, in the ground state of ttt-DPH.