  Production of ensembles of $\alpha$-particle triples associated with the
Hoyle state (the second excited state of the ${}^{12}$C nucleus) in peripheral
dissociation of relativistic ${}^{12}$C nuclei is studied. Stacks of nuclear
track emulsion pellicles exposed to ${}^{12}$C with an energy from hundreds MeV
to a few GeV per nucleon serve as the material for studies. The Hoyle state
decays are reconstructed via measurement of emission angles of $\alpha$
particles with the precision sufficient for identification of the unstable
${}^{8}$Be nucleus. The estimate of the contribution of Hoyle's state to the
${}^{12}$C $\to$ 3$\alpha$ dissociation is 10-15\%.
