@Chiu2016Classification; @Armitage2018Weyl]. Study of such phenomena is being extensively used as a new tool for classifying phases of matter which can not be distinguished by broken symmetries. Many topological insulators arise in systems of weakly interacting fermions which feature a bulk gap, and topological superconductors are similarly described by the fermionic quasiparticle excitations of a BCS superconductor.

Key aspects of these topological phases are the symmetries possessed by the material in question. If a gapped material possesses only a charge conservation symmetry, it may only realize an integer quantum Hall effect [@Thouless1982Quantized; @Avron1983Homotopy] characterized by a ${\mathbb{Z}}$ topological index. However, in the presence of other non-spatial symmetries, such as time-reversal or particle-hole symmetry, many other topological phases are possible [@Kane2005Topological; @Qi2009Time; @Schnyder2008Classification]. Examples of such phases include, the ${\mathbb{Z}}_2$ two-dimensional and three-dimensional topological insulators [@Hasan2010Colloquium; @Qi2011Topological; @Kane2005Quantum; @Kane2005Topological; @Konig2007Quantum; @FuKaneMele2007Topological; @Moore2007Topological; @Roy2009Topological], and one-dimensional and two-dimensional topological $p$-wave superconductors [@kitaev2001unpaired; @Read2000Paired].

Many materials in nature are however also characterized by spatial crystalline symmetries which emanate from their crystallographic structure. Over the past several years, these space group and point group symmetries of crystalline matter have been theoretically predicted to host a large and diverse variety of topological phases [@Mong2010Antiferromagnetic; @Fu2011Topological; 