They're part of the Western (Catholic) tradition as well, but less frequently encountered: during the Litany of the Saints that precedes ordination to the pries

They're part of the Western (Catholic) tradition as well, but less frequently encountered: during the Litany of the Saints that precedes ordination to the priesthood those to be ordained are prostrate; the ministers at the start of the Good Friday liturgy lie prostrate before the altar; and a few other special contexts.