12 v DC relay coil shows resistance in both ways 86 and 85 or 85 and 86. Why?
A diode 1N4001 is added in parallel to the coil.

Your meter (on a low ohm scale) might inject 1 mA into the &quot;thing&quot; it connects to in order to determine resistance. 100 ohms (the relay coil) and 1 mA produces a potential difference of 0.1 volts and this is way lower than what any normal silicon diode needs to start any meaningful conduction. So the diode appears open circuit.

Is not the relay supposed to show resistance only in one direction?

If the diode were wired in series then this would be the case but, you have the diode wired in parallel.

Edit - diode current at low voltages

The above is for a 1N4148 diode (rather than a 1N4001) because the data is available and therefore it can be extrapolated (as I have done in red). So, 0.1 volts divided by 40 nA = 2.5 MΩ and, compared to 100 ohms, it conducts 0.004 % of the current.