Motivic Complexes of Weight Three and Pairs of Simplices in Projective 3-Space

0. Introduction. 1. Double scissors congruence groups and polylogarithms. 2. Different versions of polylogarithmic complexes. 2.1. The B-groups: Iterative universal definition. 2.2. The B-groups: Configurations of points. 2.3. The B -groups: Explicit definition using cross ratio. 2.4. Bloch group B3 (F ) and generalized cross ratio. 3. Isomorphisms between An 6n and geometric candidates of L&n(F). 3.1. The maps an : An 6n Bn , n=2, 3. 3.2. Proof of a3(63)=0. 3.3. The maps ln : Bn An 6n , n=2, 3. 3.4. Multiple polylogarithmic pairs of weight three. 3.5. Proof of Proposition 3.15: l3 is well defined. 3.6. Injectivity of ln : Bn An 6n , n=2, 3. 3.7. Surjectivity of ln : Bn An 6n , n=2, 3. 4. A byproduct: An isomorphism of two complexes.