In the context of the search for triples of relativistic $alpha$-particles in the Hoyle state, the analysis of available data on the dissociation of the nuclei ${}^{12}$C, ${}^{16}$O and ${}^{22}$Ne in the nuclear emulsion was carried out. The Hoyle state is identified by the invariant mass calculated from pair angles of expansion in $alpha$-triples in the approximation of the conservation of the momentum per nucleon of the parent nucleus. The contribution of the Hoyle state to the dissociation of ${}^{12}$C $to$ 3$alpha$ is 11%. In the case of the coherent dissociation of ${}^{16}$O $to$ 4$alpha$ it reaches 22% when the portion of the channel ${}^{16}$O $to$ 2${}^{8}$Be is equal to 5%.
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