Hello hera, Kevin here, the guy with a million paphs. :P
Jay has given you some good info on paphs (
to you Jay). But I'd like to clarify something regarding the term "complex." The term is used for 2 different things: on the one hand the term refers to any hybrid (paph or other) whose parents are 2 hybrids or a hybrid and a species. Orchid hybrids essentially fall into 2 categories, "primary hybrids" meaning a hybrid made between 2 species and "complex hybrids" meaning essentially everything else.
On the other hand, with paphs, the term is also used to refer to a specific type of paph or group of paphs characterized by large round flowers usually with a shiny, waxy, or plastic-like texture and very firm substance. Here's a picture of a group of this type of paphs:
http://www.orquideas.com/new/Oc2000/...ouse_Paphs.jpg These types of paphs are also refered to as "exhibition" paphs, "bulldog" paphs, or "frog" or "toad" paphs.
Because of the potential for confusion (especially among new growers) that can arise form the same term (complex) referring to two different things, I prefer to call this group of paphs "exhibition" paphs and I encourage folks to avoid using the term "complex paphs" because it is easily confused with "complex hybrid." Case in point: your paph (which is lovely by the way - I am quite fond of fairrieanum and its hybrids) is a "complex hybrid" meaning it contains more than 2 species and/or hybrids but it is not a "complex paph"; it's not an "exhibition paph".
I hope that's helpful.