  Carbon, as one of the most common element in the earth, constructs hundreds
of allotropic phases to present rich physical nature. In this work, by
combining the ab inito calculations and symmetry analyses method, we
systematically study a large number of allotropes of carbon (703), and
discovered 315 ideal topological phononic materials and 32 topological
electronic materials. The ideal topological phononic nature includes single,
charge-two, three, four Weyl honons, the Dirac or Weyl nodal lines phonons, and
nodal surfaces phonons. And the topological electron nature ncludes topological
insulator, (Type-II) Dirac points, triple nodal points, the Dirac (Weyl) nodal
lines, quadratic nodal lines and so on. For convenience, we take the uni in SG
178 and pbg in SG 230 as the examples to describe the topological features in
the main. We find that it is the coexistence of single pair Weyl phonons and
one-nodal surfaces phonons in the uni in SG 178, which can form the single
surface arc in the (100) surface BZ and isolated double-helix surface states
(IDHSSs)in the (110) surface BZ. In topological semimetal pbg in SG 230, we
find that the perfect triple degenerate nodal point can be found in the near
Fermi level, and it can form the clear surface states in the (001) and (110)
surface BZ. Our work not only greatly expands the topological features in all
allotropes of carbon, but also provide many ideal platforms to study the
topological electrons and phonons.
