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Since graphite is anisotropic electrical conductivity, won't it be possible to make it an insulator instead? Like manufacturing it such that the plates of carbon atoms are mostly parallel to one another.

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Tempting, but no. Graphite is of course less conductive perpendicular to the basal plane but still boasts a conductivity of 330 S/m in that direction, https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity. Electrons can "jump" fairly easily from one pi-electron "layer" to the next.

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