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In some insulators, corner charges are fractionally quantized, due to thetopological invariant called a filling anomaly. The previous theories offractional corner charges have been mostly limited to two-dimensional systems.In three dimensions, only limited cases have been studied. In this study, wederive formulas for the filling anomaly and the corner charge in variouscrystals with all the tetrahedral and cubic space groups. We discuss that thequantized corner charge requires the crystal shapes to be vertex-transitivepolyhedra. We show that the formula of the filling anomaly is universally givenby the difference between electronic and ionic charges at the Wyckoff position1a. The fractional corner charges appear by equally distributing the fillinganomaly to all the corners of the crystal. We also derive the k-space formulasfor the fractional corner charge. In some cases, the corner charge is notdetermined solely from the irreps at high-symmetry k-points. In such cases, weintroduce a new Z2 topological invariant to determine the corner charge.

General corner charge formulas in various tetrahedral and cubic space groups