We predict the existence of triple point fermions in the band structure of several half-Heusler topological insulators by ab initio calculations and the Kane model. We find that many half-Heusler compounds exhibit multiple triple points along four independent C3 axes, through which the doubly degenerate conduction bands and the nondegenerate valence band cross each other linearly nearby the Fermi energy. When projected from the bulk to the (111) surface, most of these triple points are located far away from the surface ¯ Γ point, as distinct from previously reported triple point fermion candidates. These isolated triple points give rise to Fermi arcs on the surface, that can be readily detected by photoemission spectroscopy or scanning tunneling spectroscopy. The discovery of topological insulators (TIs) [1, 2] has generated much interest in the search for other novel topological states in condensed matter physics and materials science. As quasiparticle analogues of elementary particles of the standard model, Dirac fermions [3-6] and Weyl fermions [7-14] have recently been found in several materials (see reviews Refs. 15 and 16). Both Dirac and Weyl fermions exhibit Fermi arcs, unclosed Fermi surfaces, on the boundary, as a hallmark for the experimental detection. More recently, several exotic types of fermions, which do not have elementary particle counterparts, have been theoretically predicted as quasiparticle excitations near certain band crossing points that are protected by specific space-group symmetries [17, 18]. In particular, triple point (TP) fermions have been predicted in many materials with triply degenerate band crossing points [19-25]. These predictions have stimulated intensive experimental studies to search for their signatures, for example, using angle-resolved photoemission spectroscopy (ARPES) [26] and transport properties [27]. TPs can be viewed as an intermediate phase between fourfold degenerate Dirac points and twofold degenerate Weyl points. They also give rise to Fermi arcs when projected onto certain specific crystal facets. However, the detection of TP-induced Fermi arcs remains challenging from the material point of view. A pair of TPs are protected by the C 3v symmetry group (generated by a C 3 rotation and a σ v mirror operation) in certain compounds [19-24], for example, tensile-strained HgTe [19], MoP [20], and antiferromagnetic (AFM) half-Heusler compounds (e.g. GdPtBi) [24]. Even presuming that samples can be grown, the natural cleavable surface is usually the facet that is perpendicular to the C 3 axis. Consequently, two TPs at the unique C 3 axis are projected to the same ¯ Γ point of the surface Brillouin zone (BZ), resulting in the disappearance of Fermi arcs, as shown in a recent ARPES measurement on MoP [26]. Therefore, TP materials with easily measurable Fermi arcs are still required for the final experimental verification of TP fermions. In this work, we predict the existence of multiple TPs in several half-Heusler compounds in which the detection of Fermi arcs by ARPE...