  Traditional topological materials belong to different Altland-Zirnbauer
symmetry classes (AZSCs) depending on their non-spatial symmetries. Here we
introduce the notion of hybrid symmetry class topological insulators (HSCTIs):
A fusion of two different AZSC topological insulators (TIs) such that they
occupy orthogonal Cartesian hyperplanes and their universal massive Dirac
Hamiltonian mutually anticommute. The boundaries of HSCTIs can also harbor TIs,
typically affiliated with an AZSC different from the parent ones. As such, a
fusion between planar quantum spin Hall and vertical Su-Schrieffer-Heeger
insulators gives birth to a three-dimensional HSCTI, accommodating quantum
anomalous Hall insulators and quantized Hall conductivity on the top and bottom
surfaces. We extend this construction to encompass crystalline HSCTI and
topological superconductors, and beyond three dimensions. Possible
(meta)material platforms to harness HSCTIs are discussed.
