  We propose from first-principles calculations that spin-orbit-free materials
in the $RE_8\mathrm{Co}X_3$ group ($RE$ = rare earth elements, $X$ = Al, Ga, or
In) are ideal spinless Dirac semimetals whose Fermi surfaces are fourfold
degenerate band-crossing points (without including spin degeneracy). Despite
the lack of space inversion symmetry in these materials, Dirac points are
formed on the rotation-symmetry axis due to accidental degeneracies of two
bands corresponding to different 2-dimensional irreducible representations of
$C_{6v}$ group. The surface states have two midgap bands emanating from the
projection in the surface Brillouin zone of the bulk Dirac points, in
accordance with nontrivial Zak phases for each glide sector. We also
investigate, through first-principles calculations and effective model
analysis, various phase transitions caused by lattice distortion or elemental
substitutions from the Dirac semimetal phase to distinct topological
semimetallic phases such as nonmagnetic linked-nodal-line and Weyl semimetals
(characterized by the second Stiefel-Whitney class) and ferromagnetic Weyl
semimetals.
