What are the different types of conjoined twins?

Conjoined twins are categorized by a set of adjectives ending with the suffix "-pagus" from the Greek word for "fixed". Early teratologists such as Ambroise Pare and Geoffrey St. Hillaire were among the first to identify and name the various types of conjoined twins. Many actual sets of twins do not fit perfectly into any of these classifications, and the terms are often combined to describe these twins.