We name AB4 polytope genera (the "general shape" without indices) using existing IUPAC nomenclatural "polyhedral symbols" as outlined in the "Red Book" section IR-9.3.2.1, augmenting where necessary with additional forms devised in an analogous way. Here, we introduce the TCT-4 "tetragonally compressed tetrahedral" and TET-4 "tetragonally elongated tetrahedral" polytope genera -each formed by compressing or elongating a T-4 polytope, respectively, along an S4 axis. Both TCT-4 and TET-4 exhibit D2d symmetry. The GYP-4 "gyfu planar" polytope genus (named for the Anglo-Saxon rune) has a rectangular X-shaped planar geometry of D2h symmetry. The TT-4 "twisted tetrahedral" polytope genus exhibits D2 symmetry and results from a digonal twist along an S4 axis of the T-4, TCT-4, TET-4, SP-4, and GYP-4 genera. The SL-4 "symmetric fusion" genus in the AB4 T-4 E-mode configuration space has the two pairs of coincident B-atom unit vectors forming a symmetric linear arrangement and exhibits D∞h symmetry. All are shown in Fig. . Note that there are numerous other possible 4-vertex polytope genera in the full 5-dimensional 32 AB4 configuration space, but these require a non-zero t2-symmetric contribution and do not exhibit at least D2 symmetry.