Michael below is correct. A condex is a two unit condominium. The legal documents will call for Condo Trust with each unit owner as owning 50% of the trust. Normally the grounds around the property is common area. The unit owner usually owns their half of the dwelling from the walls in. Every complex can have different rules.
I am a mortgage person so my comments about condexes comes from a financing poit of view.
The more current issues with a condex is that often the owners have ignored the condo document requirements and have been treating their property as if they were living in single family homes. Some of them honestly do not know that they own part of a condominium. This is usually not a problem until they try to sell the units. They may not be paying condo fees for common expenses. Their insurance coverage often names the unit owner as the insured instead of the Condo Association. So when a new buyer tries to finance the property a lot of changes have to be made.
The benefits of a condex is that its almost like living in a single family. The condo fees can be minimal to cover the master insurance policy and some funds used for capital imrpovements that will be needed in the future such as possibly the replacement of a roof, repainting the exterior or the repaving of a common driveway. The concern for a lender is that what happens when these expenses come up and there are no funds put away in a reserve account. Hopefully each unit owner will be able to come up with their share of the costs.
So if you are looking to purchase a condex, make sure your lender knows this so that they can make sure you are pre-approved for the loan programs that will cover these type of properties. They can also make sure that these properties are FHA or FNMA approved or approvable.