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Abstract An unusual class of equal massp-wave universal trimers with symmetry $L^{\mathrm{\Pi }}=1^{\pm }$is identified, for both a two-component fermionic trimer withs- andp-wave scattering length close to unitarity and for a one-component fermionic trimer atp-wave unitarity. Moreover, fermionic trimers made of atoms with two internal spin components are found for $L^{\mathrm{\Pi }}=1^{\pm }$, when thep-wave interaction between spin-up and spin-down fermions is close to unitarity and/or when the interaction between two spin-up fermions is close to thep-wave unitary limit. The universality of thesep-wave universal trimers is tested here by considering van der Waals interactions in a Lennard–Jones potential with different numbers of two-body bound states; our calculations also determine the value of the scattering volume or length where the trimer state hits zero energy and can be observed as a recombination resonance. The faux-Efimov effect appears with trimer symmetry $L^{\mathrm{\Pi }}=1^{-}$when the two fermion interactions are close top-wave unitarity and the lowest $1/R^2$coefficient gets modified, thereby altering the usual Wigner threshold law for inelastic processes involving three-body continuum channels.