Simulation of fermionic relativistic physics (such as Dirac and Weyl points) has led the dicovery of versatile and exotic phenomena in photonics, of which the optical-frequency realization is, however, still a challenging aim. Here we discover that the commonly-used woodpile photonic crystals for optical-frequency applications host novel fermionic relativistic degeneracies: a Dirac linenode and a topological quadratic degeneracy point, as {em guaranteed} by the nonsymmorphic crystalline symmetry. By reducing the space symmetry, type-II Dirac/Weyl points emerge as the descendants of the quadratic degeneracy point. These exotic optical waves mimicking the physics of unconventional fermionic relativistic waves and hosting anomalous optical properties in subwavelength, all-dielectric photonic crystals could open a new avenue for future optical science.
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