Hilbert's third problem asks when two polytopes can be cut up and the parts rearranged to produce equal polytopes. This notion of equivalence is called “scissors congruence”. An invariant of scissors congruence is the Dehn invariant, which is a tensor product of the faces in the polytope and the angles between those faces. Goncherov constructed a cube of iterations of these Dehn invariants, and conjectured that the total cofiber of the cube is related to the complex algebraic K-theory. Campbell and Zakharevich constructed a map between them when the underlying geometry is spherical or hyperbolic.