  We use Pure Spinor string theory to construct suitable kinematical factors
which explicitly satisfy the Kleiss-Kuijf (KK) relations. Using the formula
conceived by Bern et al. and employed by us for 4- and 5-point amplitudes in a
previous work, we are able to compute the 6-point supergravity amplitude from
the corresponding SYM building blocks given by Mafra et al.. We derive the KK
and Bern-Carrasco-Johansson (BCJ) identities from the BRST invariance and we
discuss the relations between Bern et al. building blocks and those of Mafra et
al..
