  Carbon enjoys a vast number of allotropic forms, each possessing unique
properties determined by the lattice structures and bonding characters. Here,
based on first-principles calculations, we propose a new three-dimensional
carbon allotrope--hC28. We show that hC28 possesses exceptional energetic,
dynamical, thermal, and mechanical stability. It is energetically more stable
than most other synthesized or proposed carbon allotropes. The material has a
relatively small bulk modulus, but is thermally stable at temperatures as high
as 2000 K. The structural, mechanical, x-ray diffraction, and electronic
properties are systematically investigated. Particularly, we show that its
low-energy band structure hosts multiple unconventional emergent fermions,
including the quadratic-contact-point fermions, the birefringent Dirac
fermions, and the triple-point fermions. We construct effective models to
characterize each kind of fermions. Our work not only discovers a new carbon
allotropic form, it also reveals remarkable mechanical and electronic
properties for this new material, which may pave the way towards both
fundamental studies as well as practical applications.
