Motility-induced phase separation (MIPS) is a purely non-equilibrium
phenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and higher order structures at the interfacial region, whose underlying physics remains poorly understood. Starting with a model of MIPS in which all many-body interactions are captured by an effective speed function and an effective pressure function that depend solely on the local particle density, I derive analytically an infinite set of integral formulae for the ordering structures at the interface. I then test these integral formulae by applying them to numerical data from direct particle dynamics simulation and find that they remain valid with a high accuracy.