The first question is what type of property are these properties and how & when did you acquire them. Are they rental properties or personal properties and is there going to be any attempt to equalize the value of your respective interests in the properties given & received. So the second question is whether or not you have a taxable exchange or gifts to one another.
The rules relate to a taxable transaction as they apply to a sale or exchange.
So each of you would in essence have an exchange (treated as a sale) of each of your 1/3 interests in the properties that you are giving up measured by the difference between 2/3 of the value of the property you are receiving and your tax basis in the value of your 1/3 interest in the properties you are giving up.
You have the same exchanges treated as gifts.
Either way, the value that would be used is the properties' fair market value at the time the properties are exchanged. Your cost or tax basis (same thing) would be determined based upon how you acquired the properties. If you inherited the properties (which is why you each have an equal 1/3 interest in each property), your tax basis would be equal to the properties fair market value at the date of death of the decedent.
So, you need to expand on the facts, how & when you acquired the properties & what type of property is each property. Also, are there offsets to equalize the values among the three of you when the properties are exchanged?