  Space-time light structuring has emerged as a very powerful tool for
controlling the propagation dynamics of pulsed beam. The ability to manipulate
and generate space-time distributions of light has been remarkably enhanced in
past few years, letting envision applications across the entire spectrum of
optics. Space-time optical wavepackets manipulated up to now are usually
two-dimensional objects (one space dimension and time) whose mode-resolved
spectra lie in a conical section. Using simple symmetry and invariance
principles, we show that such wavepackets are particular cases of more general
three-dimensional structures whose space-time frequencies lie on quadric
surfaces. Our proposed framework allows here classifying space-time wavepackets
localized in all dimensions, in any group-velocity dispersion regime, both in
bulk and waveguides. Particular emphasis is placed on orbital angular
momentum-carrying space-time wavepackets. This unprecedented theoretical
approach opens the way for versatile synthesizing of space-time optics.
