  Using Totaro-Bloch-Kriz's linear fractional cycles Gangl and Muller-Stach
recently prove the 5-term relations for the dilogarithm in Bloch's higher Chow
group CH^2(F,3) and the Kummer-Spence relations in some group G(F) over an
arbitrary field F where G(F) is isomorphic to CH^3(F,5) up to torsions under
the Beilinson-Soule vanishing conjecture that CH^2(F,n)=0 for n>3. In this
paper we show that Goncharov's 22-term relations for the trilogarithm also hold
in G(F).
