Local congruence of chain complexes

Abstract

Figure 1: Cellular 3-complexes: (a) two rotated cuboid grids 5 × 5 × 5; (b) exploded set of intersected 3-cells. It is interesting to note that #V -#E + #F = 1192-3182+2824 = 834 = #C, according to the Euler characteristic χ 0 − χ 1 + χ 2 − χ 3 = 0 of a polyhedral partition of the 3-sphere. The images are generated by the Julia 3D graphics package https://github.com/cvdlab/ViewerGL.jl.