The sestina is a very strict verse form, consisting of six six-line stanzas or sextets/sestets followed by a three-line tercet called the envoy. The sestina incorporates six keywords, one of which ends every line. If you assign a number to each keyword, and then write these out in a six by six grid (e.g. a line across for each of the six stanzas), you’ll see that the set pattern for the line endings makes a magic square.
The sestina's been around since the Middle Ages, with poets such as Philip Sidney and Auden enjoying the intellectual challenge it presents, both for the poet and the reader, particularly since this particular structure often takes a while for the reader to decode - you can see that there's some rule/pattern that's being followed, but (especially for the less naturally mathematical amongst us) it can take some time before you work out exactly what the pattern is. It's always struck me as being rather like change ringing for bells.
One lovely modern example of a sestina is by Elizabeth Bishop:
A Miracle for Breakfast - Elizabeth Bishop
At six o'clock we were waiting for coffee,
waiting for coffee and the charitable crumb
that was going to be served from a certain balcony
--like kings of old, or like a miracle.
It was still dark. One foot of the sun
steadied itself on a long ripple in the river.
The first ferry of the day had just crossed the river.
It was so cold we hoped that the coffee
would be very hot, seeing that the sun
was not going to warm us; and that the crumb
would be a loaf each, buttered, by a miracle.
At seven a man stepped out on the balcony.
He stood for a minute alone on the balcony
looking over our heads toward the river.
A servant handed him the makings of a miracle,
consisting of one lone cup of coffee
and one roll, which he proceeded to crumb,
his head, so to speak, in the clouds--along with the sun.
Was the man crazy? What under the sun
was he trying to do, up there on his balcony!
Each man received one rather hard crumb,
which some flicked scornfully into the river,
and, in a cup, one drop of the coffee.
Some of us stood around, waiting for the miracle.
I can tell what I saw next; it was not a miracle.
A beautiful villa stood in the sun
and from its doors came the smell of hot coffee.
In front, a baroque white plaster balcony
added by birds, who nest along the river,
--I saw it with one eye close to the crumb--
and galleries and marble chambers. My crumb
my mansion, made for me by a miracle,
through ages, by insects, birds, and the river
working the stone. Every day, in the sun,
at breakfast time I sit on my balcony
with my feet up, and drink gallons of coffee.
We licked up the crumb and swallowed the coffee.
A window across the river caught the sun
as if the miracle were working, on the wrong balcony.