  Quasitopological electromagnetism has an important influence on the strong
gravity of dyonic black hole. For example three photon spheres with one being
stable are found and we wish to test them with the observed black hole shadow.
We are primarily concerned with the thermodynamics and phase transition for a
dyonic anti-de Sitter (AdS) black hole when the quasitopological
electromagnetism is included.Unlike in a black hole solution without
quasitopological electromagnetism, we observe a triple point phase structure by
varying the coupling parameters. Of particular interest, for certain parameter
values, two separate coexistence curves are present, which is an additional
novel phase structure that is absent in a black hole solution without
quasitopological electromagnetism. The critical exponents share the same values
as mean field theory. These results uncover the intriguing properties of dyonic
AdS black holes with quasitopological electromagnetism from a thermodynamic
point of view.
