While pyrite-type PtBi_{2} with a face-centered cubic structure has been predicted to be a three-dimensional (3D) Dirac semimetal, experimental study of its physical properties remains absent. Here we report the angular-dependent magnetoresistance measurements of a PtBi_{2} single crystal under high magnetic fields. We observed extremely large unsaturated magnetoresistance (XMR) up to (11.2×10^{6})% at T=1.8  K in a magnetic field of 33 T, which is comparable to the previously reported Dirac materials, such as WTe_{2}, LaSb, and NbP. The crystals exhibit an ultrahigh mobility and significant Shubnikov-de Hass quantum oscillations with a nontrivial Berry phase. The analysis of Hall resistivity indicates that the XMR can be ascribed to the nearly compensated electron and hole. Our experimental results associated with the ab initio calculations suggest that pyrite PtBi_{2} is a topological semimetal candidate that might provide a platform for exploring topological materials with XMR in noble metal alloys.

Triply degenerate point (TP) fermions in tungsten–carbide-type materials (e.g., MoP), which represent new topological states of quantum matter, have generated immense interest recently. However, the TPs in these materials are found to be far below the Fermi level, leading to the TP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically predict the existence of TP fermions with TP points close to the Fermi level in trigonal layered PtBi2 by ab initio calculations, and experimentally verify the predicted band topology by magnetotransport measurements under high magnetic fields up to 40 T. Analyses of both the pronounced Shubnikov–de Haas and de Haas–van Alphen oscillations reveal the existence of six principal Fermi pockets. Our experimental results, together with those from ab initio calculations, reveal the interplay between transport behaviors and unique electronic structures, and support the existence of TP fermions in trigonal layered PtBi2.