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Well, to be perfectly honest, if I had my druthers, I'd recognize six major
stem-based groups ("classes") of tetrapods, anchored on typical living
representatives:
Batrachopsida ("froggy-looking things"): {_Rana_>_Homo_, _Chelone_,
_Vipera_,
_Crocodylus_, _Passer_}. Would currently include frogs, salamanders,
caecilians, etc.
Theropsida ("beasty-looking things"): {_Homo_>_Rana_, _Chelone_, _Vipera_,
_Crocodylus_, _Passer_}. Would currently include mammals, other
therapsids,
"pelycosaurs".
Chelonopsida ("turtlish-looking things"): {_Chelone_>_Rana_, _Homo_, etc.}.
Would include turtles and whatever the heck they're most closely related
to.
Herpetopsida ("snaky-looking things"): {_Vipera_>_Rana_, _Homo_, etc.}.
Would include snakes, other lizards, tuataras, etc.
Crocodilopsida ("crocodilish-looking things"): {_Crocodylus_>_Rana_,
_Homo_,
etc.}. Would include crocodilians as well as aetosaurs, rauisuchians,
phytosaurs, etc. (depending on just where turtles fit in).
Ornithopsida ("birdy-looking things"): {_Passer_>_Rana_, _Homo_, etc.}.
Would include birds and other dinosaurs, "lagosuchians", and perhaps
pterosaurs.
Other "classes" could (but need not necessarily) be named analogically for
groups that do not fit into any of the above clades.
--Nick P.