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The Collaborative International Dictionary
Double acrostic

Acrostic \A*cros"tic\, n. [Gr. ?; ? extreme + ? order, line, verse.]

  1. A composition, usually in verse, in which the first or the last letters of the lines, or certain other letters, taken in order, form a name, word, phrase, or motto.

  2. A Hebrew poem in which the lines or stanzas begin with the letters of the alphabet in regular order (as Psalm cxix.). See Abecedarian.

    Double acrostic, a species of enigma (crossword puzzle), in which words are to be guessed whose initial and final letters form other words.

Wiktionary
double acrostic

n. A poem whose stanzas, except the first two, are clues for words. The initial letters of these words, in order, form a word clued by the first stanza; the final letters, the second stanza.