  Topological manipulation of waves is at the heart of the cutting-edge
metamaterial researches. Quadrupole topological insulators were recently
discovered in two-dimensional (2D) flux-threading lattices which exhibit
higher-order topological wave trapping at both the edges and corners. Photonic
crystals (PhCs), lying at the boundary between continuous media and discrete
lattices, however, are incompatible with the present quadrupole topological
theory. Here, we unveil quadrupole topological PhCs triggered by a twisting
degree-of-freedom. Using a topologically trivial PhC as the motherboard, we
show that twisting induces quadrupole topological PhCs without flux-threading.
The twisting-induced crystalline symmetry enriches the Wannier polarizations
and lead to the anomalous quadrupole topology. Versatile edge and corner
phenomena are observed by controlling the twisting angles in a lateral
heterostructure of 2D PhCs. Our study paves the way toward topological
twist-photonics as well as the quadrupole topology in the quasi-continuum
regime for phonons and polaritons.
