theoretically complete and rigorous approach is the formulation of the crystalline classification problem using twisted equivariant K-theory [@freed2013twisted; @Morimoto2013Topological; @Shiozaki2014Topology; @Hsieh2014CPT; @Shiozaki2016Topology; @Shiozaki2017Topological; @Trifunovic2017Bott; @shiozaki2018atiyah; @Geier2018Second; @trifunovic2018higher; @okuma2018topological]. Within twisted equivariant K-theory the crystallographic group action on the Hamiltonian is encoded by a twist on the Brillouin zone (BZ) which serves as the base space of the K-group [@Shiozaki2017Topological]. This approach was successful in obtaining a complete classification of all topological invariants of order-two magnetic space group crystals [@Morimoto2013Topological; @Shiozaki2014Topology] as well as of all wallpaper group crystals [@Shiozaki2017Topological; @graph]. However, due to the mathematically challenging nature of the paradigm, ongoing works [@shiozaki2018atiyah] are still being carried in an attempt to calculate all topological invariants of all crystallographic symmetry groups.

Herein, we follow the approach of Freed and Moor \[\], Morimoto and Furusaki \[\], and Shiozaki, Sato, and Gomi \[\]. We focus on bulk topological invariants which are akin to the strong topological invariants of topological insulators and superconductors with non-spatial symmetries [@kitaev2009periodic; @schnyder2009classification; @ryu2010topological; @franz2013topological; @witten2015three; @abramovici2012clifford]. We generalize the Clifford algebra classification scheme (see Fig. \[fig:diag1\]) by incorporating the point group symmetry actions into the algebra of symmetries generated by the non-spatial symmetries, and a Hamiltonian compatible with 