| Summary: | We studied a non-interacting <inline-formula><math display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>/<i>V</i>-type dice model composed of three triangular sublattices. By considering the isotropic nearest-neighbor hoppings and the next-nearest-neighbor hoppings with the phase, as well as the quasi-staggered on-site potential, we acquired the full phase diagrams under the different fillings of the energy bands. There are abundant topological non-trivial phases with different Chern numbers <inline-formula><math display="inline"><semantics><mrow><mi>C</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow></semantics></math></inline-formula>, as well as higher ones <inline-formula><math display="inline"><semantics><mrow><mo>±</mo><mn>2</mn><mo>,</mo><mo>±</mo><mn>3</mn></mrow></semantics></math></inline-formula> and a metal phase in several regimes. In addition, we also checked the bulk–edge correspondence of the system by analyzing the edge-state energy spectrum.
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