If we're getting into the detail of Logopolis, the Doctor says they have to measure the real police box (for comparison with the TARDIS) in all 30-plus dimensions, implying that a real-world object does have the full multi-dimensional set (the implication is that the TARDIS can't change because of a mismatch between the form she's aiming for, and the reality she's achieved, that needs to be added into the BTC calculations to resolve the mismatch. This doesn't really make sense, unless the TARDIS had always patterned herself on that obsolete 1981 police box on the Barnet bypass, not one in 1963 east London around the time of An Unearthly Child).
Of course, we now know that it's just that she likes looking like a police box. The Doctor didn't know her as well back then so he was trying to solve the Chameleon Circuit fault through brute force mathematics, rather than just talking to her...