  Designing metamaterials with the required band structure, topology and
chirality using nano-fabrication technology revolutionises modern science and
impacts daily life. The approach of this work is, however, different. We take a
periodic sequence, i.e., metacrystal, of the dissipative optical solitons
rotating in a single ring microresonator and demonstrate its properties as of
the electromagnetic metamaterial acting in the radio to terahertz frequency
range. The metacrystal unit cell consists of the bound pair of solitons, and
the distance between them is used as a control parameter. We are reporting the
soliton metacrystal band structure and its topological properties. The latter
is confirmed by the existence of the $\pi$ steps experienced by the crystal
phonons' geometrical (Zak) phase. Furthermore, we found the phononic edge
states in the metacrystals with defects made by removing several solitons.
Optical frequency combs corresponding to the soliton metacrystals reveal the
spectral butterfly pattern serving as a signature of the spatio-temporal
chirality and bearing a resemblance to the butterfly wings illustrating natural
occurrences of chirality.
