A three-phase connection requires three hot wires, one for each phase of the current. Air conditioners that operate on single-phase current will require either a hot and neutral connection, or a connection with two hot wires. There is no way, without significant modification, to connect a single-phase air conditioner to all three-phases of a three-phase supply.
Most three-phase supply systems include connections for lighting circuits and single-phase appliances. These systems exist in both residential apartment buildings and in some commercial environments to operate appliances such as air conditioners.
The three-phase current supply in certain apartment buildings provides two phases of current, plus a neutral wire, to each apartment. The current between any hot wire and a neutral wire is approximately 120 volts and is a single-phase circuit.
A second type of circuit found in apartment buildings comes from the three-phase supply for operating appliances such as electric ranges and larger air conditioners. Two wires from the three-phase supply provide a total of 208 volts.
Manufacturers design and build appliances, including air conditioners, to operate on specific voltages. A typical window air conditioner may require either 120 or 208/230 volts of single-phase current. Most central air conditioning units require 208/240 volts of current.
Manufacturers also take into consideration that the appliances they build will operate in different types of environments. Some utility customers have 120-240 volt single-phase electrical systems; others have 120-208 volt systems derived from a three-phase supply. Still others -- mainly commercial customers -- have 120-230 volt systems, also from a three-phase supply.
An air conditioner designed to run on single-phase current won't have any trouble operating off a three-phase supply, as long as it connects to the correct voltage. In an apartment building, a 120-volt circuit is a single-phase circuit. A 208- or 230-volt circuit in the same building will operate single-phase appliances -- including air conditioners -- designed for the higher voltage, even though the voltage comes from a three-phase supply.
The connection to the air conditioner does have to meet the appliance's voltage requirements. It is important to note that in some commercial three-phase systems, not all the hot wires are the same. Some hot-to-hot connections provide a much higher voltage than 230 volts, and some hot-to-neutral connections can exceed 120 volts.