We compute the $E_2$ pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, using cell decompositions such that any group element that fixes a cell setwise also fixes it pointwise. We provide a detailed description of the implementation for computing the $E_2$ pages of AHSS. Under a physically reasonable assumption, we enumerate all possible $K$-groups that are compatible with the $E_2$ pages for both momentum and real-space AHSS. As a result, we determined the $K$-groups for approximately 59% of symmetry settings in three spatial dimensions.

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• Electronic structure
• Surface states
• Topological insulators
• Topological phases of matter
• Topological superconductors