  We show that the previously predicted Fermion particle that has no analogue
in the standard model of particle theory - the cubically dispersed Dirac
semimetal (CDSM) - is realized in a specific, stable solid state system that
has been made years ago, but was not appreciated to host such a unique Fermion,
composed of six Weyl Fermions, 3 with left-handed and 3 with right-handed
chirality. We identified the crystal symmetry constraints and found the space
group P63/m as one of the two that can support a CDSM, of which the
characteristic band crossing has linear dispersion along the principle axis but
cubic dispersion in the plane perpendicular to it. We then conducted a material
search using density functional theory identifying a group of
quasi-one-dimensional molybdenum mono-chalcogenide compounds A(MoX)3 (A = Na,
K, Rb, In, Tl, X = S, Se, Te) as ideal CDSM candidates. Studying the stability
of the A(MoX)3 family reveals a few candidates such as Rb(MoTe)3 and Tl(MoTe)3
that are predicted to be resilient to Peierls distortion, thus retaining the
metallic character. The combination of one-dimensionality and metallic nature
in this family provides a platform for unusual optical signature - polarization
dependent metallic vs insulating response.
