An associative container is exactly that how it is defined in STL: an unambigous mapping of one set of values in another. We did not have any intention to reinvent the wheel, so there is only a couple of specialized associative containers in the Polymake Template Library. In the most cases the standard std::map and std_ext::hash_map do their job well.

• Map
  a side product of the AVL tree implementation. You might prefer it to the standard std::map if you have a complex key type and want to make profit from an accelerated key comparator class.
• FaceMap
  a special class optimized for storing of sets of integers which have common prefixes (as they often occur as faces of a complex)