Vanishing of the polyhedral Euler-complex relations

Let $K$ be the number field, ${\cal P}$ a prime ideal in its ring of integers, and let $\gamma {\Bbb B}_d$ be a polyhedron in the Bianchi decomposition of the orbifold ${\cal Y}_1({\cal P})$. Denote by $\theta_E^{(1)}(\partial(\gamma {\Bbb B}_d))$ the element of $K_3(K_{\cal P})_{\Bbb Q}$ corresponding to the boundary of this polyhedron. Vanishing conjecture. The element

$$\theta_E^{(1)}(\partial (\gamma {\Bbb B}_d))=0.$$

This vanishing would eliminate the relations contributed by the Bianchi polyhedra in the construction of the Euler complexes and clarify the relations among the elements $\theta_E(a_1,a_2,a_3)$. The supplied text does not establish the assertion or provide evidence resolving it.