  Carbon, the basic building block of our universe, enjoys a vast number of
allotropic structures. Owing to its bonding characteristic, most carbon
allotropes possess the motif of hexagonal rings. Here, with first-principles
calculations, we discover a new metastable three-dimensional carbon allotrope
entirely composed of pentagon rings. The unique structure of this "Pentagon
Carbon" leads to extraordinary electronic properties, making it a cornucopia of
emergent topological fermions. Under lattice strain, Pentagon Carbon exhibits
topological phase transitions, generating a series of novel quasiparticles,
from isospin-1 triplet fermions, to triply-degenerate fermions, and further to
concatenated Weyl-loop fermions. Its Landau level spectrum also exhibits
distinct features, including a huge number of almost degenerate chiral Landau
bands, implying pronounced magneto-transport signals. Our work not only
discovers a remarkable carbon allotrope with highly rare structural motifs, it
also reveals a fascinating hierarchical particle genesis with novel topological
fermions beyond the Dirac and Weyl paradigm.
