Poem on a Pyramid

Math and poetry share at least one thing in common: they’re seen as obscure.

Folks tend to regard them as a bit like the Dead Sea: deep and undrinkable. Easy to float on the surface. Hard to get much further.

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But they’ve got more playful and pleasant commonalities. The precision. The puzzles. The paradoxes. Lots of great writers have made their living on the fertile borderland between poetry and mathematics: Jorge Luis Borges, Lewis Carroll, Raymond Queneau. The whole Oulipo movement aimed to harvest mathematical structures to create new poetic and literary forms.

And not long ago, I came across one of my favorite Oulipo-inspired mathematical-poetical creations: the tetrahedral pantoum.

You begin with a tetrahedron—that is to say, a triangular pyramid.

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Inscribe each of its six edges with a line of poetry.

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Each face becomes a three-line stanza.

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The tetrahedron as a whole becomes a four-stanza poem.

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In theory, each face allows for six readings (ABC, ACB, etc.), and the four faces can be arranged in 24 sequences, for a total of 144 possible poems, all close cousins. That’s too many degrees of freedom; we want each tetrahedron to induce a unique poem. And so we abide by two rules:

  1. Each stanza begins at a different vertex.
  2. Each stanza’s first line is the middle line of the stanza before, and must be traced in the same direction.

Thus, once you label your tetrahedron, the poem more or less writes itself:

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This Platonic verse form owes its invention to Enriqueta Carrington. I learnt of it while combing the archives of JoAnne Growney’s delightful blog “Intersections,” where I found myself spellbound by this example of Carrington’s:

The Goddess Works Her Loom

Until at last the pattern is fully there,
who can read the figures that she weaves?
Ixchel sits on her heels, a snake in her hair.

Who can read the figures that she weaves
as she murmurs a lullaby, spell, or prayer?
One mother rejoices, another one grieves,

as she murmurs a lullaby, spell, or prayer
while children drop like tears, or rain, or leaves.
Ixchel sits on her heels, a snake in her hair

while children drop like tears, or rain, or leaves
until at last the pattern is fully there—
one mother rejoices, another one grieves.

The magic here? It’s how form suits function. The goddess in the poem weaves a higher logic, while the mortals glimpse only inscrutable fragments. Meanwhile, the poet weaves a higher geometry, but the reader glimpses only a one-dimensional projection, cryptic fragments.

Who can read the figures that she weaves, until at last the pattern is fully there?

Good math makes you reach for pencil and paper. Good poetry, in this case, made me summon a spreadsheet. Easy to program: type in six lines, and they appear in their proper places below. Could I write a tetrahedral pantoum of my own? Or, in my clumsy hands, would the symmetries and repetitions become a lazy gimmick?

On Math I Struggle to Conceptualize

Not all structures can be seen—
even those that can be sensed
like the hum of some machine.

Even those that can be sensed,
symbols bury what they mean:
doors I knock and knock against.

Symbols bury what they mean
even when my brain’s commenced
like the hum of some machine.

Even when my brain’s commenced
not all structures can be seen:
doors I knock and knock against.

The technical phrase for this is “amateur hour.” Instead of resounding with haunting echoes, my last stanza just plods along, adding nothing: a lazy three-line oaf.

Also, whereas Carrington’s lines take on new meanings when they reappear (the “she” who “murmurs a lullaby” is at first the goddess, and later the grieving/rejoicing mothers), mine don’t.

(Not to mention the fact that brains don’t “commence.”)

All right, back to the spreadsheet for Attempt #2:


A thousand yards of empty space
where living things can tread no more;
beyond, a foe without a face.

Where living things can tread no more
they send their thoughts to interlace;
A princeling’s death ignites a war.

They send their thoughts to interlace,
to name the cause they’re dying for
beyond a foe without a face.

To name the cause, they’re dying for
a thousand yards of empty space.
A princeling’s death ignites a war.

Better, I think! In a high-school-literary-magazine kind of way, but hey, poetic beggars can’t be choosers. By shuffling commas, I’m able to freshen up several lines in their encore appearance.

The last two stanzas actually work. Now it’s only stanza #2 that feels like dead weight.

Eventually I realized that the best tribute to Carrington is perhaps not to write more poems in her format, but to carry on the project of devising new, mathematically inspired poetic forms.

Although “inspired” is perhaps not the best descriptor, here is my own contribution: the Pythagorean Haiku:

is what I call these unconventional haikus
where the syllable counts make a right triangle’s sides.

They achieve
a strange balance,
a pleasing squareness.

The first line flickers quickly
and lingers in the ear while its successors plod behind, clumsy and prosaic, but somehow linked—
linked as the hypotenuse to the legs, or as the cosmos to the ancient music of ratio.

Obviously, this is a multiplayer game, and so I welcome your thoughts (and poetical stylings) below. If you’d like the spur of a template for the tetrahedral pantoum, you can download it here. Otherwise, enjoy your Platonic solids, your poetic forms, and most of all, the intersections thereof.

EDIT: Here’s a lovely poetic experiment from Neil Calkin, very much in the same vein: a “Dodecahedral Trail” that traces out a poem from the edges of a dodecahedron.

Walking/Constructing the dodecahedral trail by Neil Calkin

10 thoughts on “Poem on a Pyramid

  1. I’ll leave a little poem with a challenge: will somebody figure out the math behind it? 😉

    Cryptic voice
    heard and then forgotten
    circles again
    sign misunderstood

    little hint: 7 😉

    1. Pattern.
      But where to look?
      Syllables in a line, perhaps?
      All classes mod p?
      This is too easy a solution, true.
      A second pattern, yet a deeper
      Generation, you might say.
      Powerful perspective.

  2. I’d feel remiss not to mention:

    “A conjecture both deep and profound
    Is whether the circle is round.
    In a paper of Erdös
    Written in Kurdish
    A counterexample is found.”

    (no tetrahedron required)

  3. Beautiful! I think your geometric poems are incredibly impressive for a first attempt.

    Jo Anne Growney’s blog is definitely one of the most comprehensive resources available, when it comes to maths and poetry.

    I recently spent some time researching people who have worked in both fields throughout history – if anyone is interested, here’s the link:


    As you pointed out Ben, there are a lot of abstract similarities between the two disciplines. I think many many students of mathematics would be incredibly surprised to hear this! Although I don’t know if it would make them more or less inclined to maths…

  4. My attempt:

    The line continues straight,
    y forever grows with x,
    until they reach infinity.

    y forever grows with x,
    faster and faster now,
    as the exponential curves.

    Faster and faster now
    their distance keeps increasing,
    until they reach infinity.

    Their distance keeps increasing,
    the line continues straight,
    as the exponential curves.

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