Multi-band superconductivity in topological semimetals are the paradigms of
unconventional superconductors. Their exotic gap structures and topological
properties have fascinated searching for material realizations and
applications. In this paper, we focus on triple point fermions, a new type of
band crossings, and we claim that their superconductivity uniquely stabilizes
spin-triplet pairing. Unlike conventional superconductors and other multi band
superconductors, such triplet superconductivity is the novel phenomena of
triple point fermions where the spin-singlet pairing is strictly forbidden in
the on-site interaction due to the Fermi statistics. We find that two distinct
triplet superconductors, characterized by the presence and absence of
time-reversal symmetry, are allowed which in principle can be controlled by
tuning the chemical potential. For the triplet superconductor with
time-reversal symmetry, we show that topologically protected nodal lines are
realized. In contrast, for time-reversal broken case, the complication of
topologically protected Bogoliubov Fermi surfaces emerges. Our theoretical
study provides a new guidance for searching triplet superconductivities and
their exotic implications.Comment: 7 pages, 3 figure