The answer is NO

This past weekend I have much enjoyed reading Mathematics:  a novel  by Jacques Roubaud  (Dalkey Archive Press, reprint 2010, translated from the French by Ian Monk); Roubaud is a mathematician, poet, and member of the OULIPO.  And here is a found poem from Chapter 1:
.
          A
          question
          posed to a
          lively colleague:

          do you tell your
          dancing partners
          that you practice
          mathematics?

For me, like so many of us -- females especially -- revelation of a connection to mathematics leads to an awkward moment, an impediment to a possible relationship.  And so we say things like "I am at the university" or "I am doing some writing" or . . .

A septina ("Safety in Numbers") -- and variations

Recall that a sestina is a 39 line poem of six 6-line stanzas followed by a 3-line stanza.  The 6-line stanzas have lines that end in the same six words, following this permutation pattern:

   123456   615243   364125
   532614   451362   246531

The final stanza uses two of the six end-words in each of its three lines.  An original pattern for these was 2-5, 4-3, 6-1 but this is no longer strictly followed.

Can sestina-like patterns be extended to other numbers?  Poet and mathematician Jacques Roubaud of the OULIPO investigated this question and he considered, in particular, the problem of how to deal with the number 7 of end-words -- for 7 does not lead to a sestina-like permutation.  Rombaud circumvented the difficulty (see Oulipo Compendium -- Atlas Press, 2005) by using seven 6-line stanzas, with end-words following these arrangements: