Forming the backbone of quantum technologies today, entanglement1,2 has been demonstrated in physical systems as diverse as photons3, ions4 and superconducting circuits5. Although steadily pushing the boundary of the number of particles entangled, these experiments have remained in a two-dimensional space for each particle. Here we show the experimental generation of the first multi-photon entangled state where both the number of particles and dimensions are greater than two. Two photons in our state reside in a three-dimensional space, whereas the third lives in two dimensions. This asymmetric entanglement structure6 only appears in multiparticle entangled states with d > 26. Our method relies on combining two pairs of photons, high-dimensionally entangled in their orbital angular momentum7. In addition, we show how this state enables a new type of ‘layered’ quantum communication protocol. Entangled states such as these serve as a manifestation of the complex dance of correlations that can exist within quantum mechanics.