I am writing a scientific paper in which I perform a mathematical operation that is illustratively called folding, which is already an established term. I now want to assign a similarly illustrative name to the product of that folding. This word should refer to the whole folded object (red) and ideally neither be usable for the process of folding (blue) or just the point of folding (crease, green), as this could confuse readers.

illustration of a folded something

I have considered the following words so far:

  • fold – while this word can indeed be used for what I need, it can also be used for the point of folding (green). Still, I consider this one of the better choices for now.

  • foldth – a neologism in analogy to warm → warmth, break → breach, grow → growth and similar. However, there are also strong → strength, wide → width and similar, which work differently. Being a new word, it cannot be confused for something else but may be confusing due to being new, in particular as the morphology behind this feels rather old and unproductive to me. Also, the ldth sequence may be difficult to pronounce for some (there is no English word containing this sequence).

  • folding – fits in analogy to build → building or scaffolding. However, it can also be applied to the process of folding (blue).

  • origami – quite illustrative, but not morphologically related to to fold. Also, it might be considered silly by readers.

  • foldee – something I would use for someone who is being folded. Yet it does not quite fit for something that is being folded. Moreover it rather describes the object of the folding, not the result (compare to examinee vs. graduate).

  • foldery – a neologism in analogy to bake → bakery, flatter → flattery and similar. Does not really fit as I would rather use it for a place where folding happens or for intensive or repeated folding.

  • folder – does not really fit as it rather describes somebody or something that folds.

I am wondering whether I missed some better option. Note that I am looking for a single word and I am open to neologisms, if they are intelligible.

  • 1
    Technically, "origami" is at least semantically related to 'fold': its literal Japanese translation is 'folded paper', though it more typically refers to the art of the folding of the paper, instead of the physical products of said artistic efforts. But, to the average English speaker unfamiliar with Japanese, the word indeed does not evoke 'fold'.
    – hBy2Py
    Commented May 7, 2015 at 14:26
  • 1
    "Fanfold" as a noun. If you formally or contextually define it it will be well enough understood. | Folderol? :-) (aka Fiddlededee) Commented May 7, 2015 at 14:31
  • 3
    What's wrong with folded? The product of folding is a folded item. Once you are finished folding your mathematical operation, the operation is folded.
    – ShemSeger
    Commented May 7, 2015 at 16:20
  • Given the significant range of suggestions provided thus far, none of which have (apparently?) met with your satisfaction, perhaps you could describe your method in a bit more detail. Perhaps some aspect of the workings of the procedure itself, over and above just your having coined folding to describe the procedure, might prompt something more like what you're seeking.
    – hBy2Py
    Commented May 8, 2015 at 11:15
  • If you pick a generic word for describing the result of a folding operation that you did not find by yourself it will not be very common and not very visual. Why not pick a simple object which commonly can be seen folded? Like a towel or a blanket – it definitely matches your picture! Bellows would be also nice and visual but more serious. Stack, fan, manifold, bundle and sheaf are nice but are already very well established and very general mathematical concepts. Commented May 8, 2015 at 12:09

24 Answers 24


I submit a neologism:

foldation would be to fold as foundation is to found.

Interestingly, I found that found has a meaning I didn’t know before,


melt and mould (metal). fuse (materials) to make glass. make (an article) by melting and moulding metal.

from which meaning the yummy French fondant comes.

The origin of fold is Germanic, not Latin which might explain why there isn’t a word for what you’re talking about. Were it French, we might already have foldant to use, or foldation for that matter.

  • Note that in another Germanic language, German, there are sevaral mechanisms available to form a straightforward neologism for what I am looking: To fold is falten, with falt being the stem; what I am looking for would then be Gefalt or Faltnis.
    – Wrzlprmft
    Commented May 9, 2015 at 8:38
  • 1
    Daresay foundry is the most commonly used English word derived from that sense of found.
    – hBy2Py
    Commented Jun 2, 2015 at 17:26
  • @Wrzlprmft - You could follow the lead of the translators of Marxism, and just pull in some German terms without translation. Commented Dec 6, 2016 at 10:39
  • Yes foldation was what popped into my mind as well.
    – Jelila
    Commented Jan 23, 2019 at 4:07
  • Fondant is gross. Fondue, however...
    – Patrick M
    Commented Feb 10, 2021 at 4:43

How about:

  • an accordion, or
  • a bellows, or even
  • a sylphon

You might also consider @Nair's (now deleted) suggestion:

  • a fan


An accordion is a well-known musical instrument, distinguished and instantly recognizable for its folded construction:

Partially folded accordion
Source: Wikipedia

It's also the name for a GUI element which can be folded out:

Accordion GUI control element
Source: Wikipedia

It's also what happens to hapless coyotes when they fall off high cliffs:

Wile E. Coyote, *accordioned* from a fall
Source: Warner Bros / Looney Tunes


Now, of course, the accordion, concretely, is the complete musical instrument: it has valves, and reeds, and sometimes a keyboard. But at its heart lies one element, the one that gives it its characteristic folds: the bellows.

A hand-bellows used for stoking fires
Source: Wikipedia

And bellows, of course, are founded on the principle of folding (and unfolding): they are the specific folded object.


Finally, since you're writing a scientific paper, you might appreciate the sylphon, which is an old name for a specific type of cylindrical metal bellows.

Metal sylphon, partially folded
Source: helenbellows.ecvv.com

I suggest it for you specifically because it was popularized in the physics community by the famous physicist John Strong, in his work "Procedures in Experimental Physics".


Another user, @Nair, had added an answer suggesting fan, but it got deleted. I think that's a fantastic suggestion:

Two folding fans; one open, one closed
Source: fashioncraft.com

Of course, each of these words shares the drawback you identified for origami: they are not morphologically derived from "fold".

  • Origami is a Japanese word and literally means "folding paper". It may not have Latin or Greek origins, but it is definitely derived from "fold".
    – Paul Rowe
    Commented May 7, 2015 at 14:33
  • 1
    @Paul I was simply quoting OP's stated concern about origami, that it is "quite illustrative, but not morphologically related to to 'fold'. Also, it might be considered silly by readers.". All my suggestions are in the same situation: they're related conceptually, but not morphologically, to the word "fold". (And in general, when the OP raises a specific concern, I try to be cognizant of that in my answers, and explicitly identify both the benefits and drawbacks of any suggestions I make). But you're right: I should have said morphological, not syntactic. I'll edit that now.
    – Dan Bron
    Commented May 7, 2015 at 14:37
  • 6
    Bravo Zulu, sir, for including a pic of Wile E. Coyote in an answer to a mathematically-themed question posted on an English help forum.
    – cobaltduck
    Commented May 7, 2015 at 14:53
  • 2
    In the UK "concertina" is used for this instead of "accordion". A similar type of musical instrument, but smaller. "Concertina'd" can also be used as a verb, e.g. "the front of the car was concertina'd in the crash".
    – alephzero
    Commented May 7, 2015 at 21:19
  • The fact that fan is a fantastic suggestion it tantamountainously tautological.
    – msouth
    Commented May 8, 2015 at 15:19

I really think you're best off sticking with folded object. It is clear and unambiguous—it doesn't need explaining. Why grasp for a neologism that really won't save much space (how many times will you use the term? Five? A dozen? A hundred? Unless you are charged by the word or using gold ink, this shouldn't be a problem.)

However, there is a word you can use (it's normally a suffix, but might be well understood as a noun if you explain it once): plex.

  • 1
    The problem with your first suggestion is that I would have to replace object with something that already is a compound term, which would negatively impact the readability of many sentences – to the extent that I would have to reformulate some of them. Compare “We now discombobulate a folded banana transmogrificator’s thingamob, which is …” to “We now discombobulate a fold’s thingamob, which is …”.
    – Wrzlprmft
    Commented May 7, 2015 at 10:50
  • 2
    Ok. How about plex? Commented May 7, 2015 at 11:15
  • I am considering it (hence a +1).
    – Wrzlprmft
    Commented May 7, 2015 at 11:20



  1. An orderly pile, especially one arranged in layers: a stack of newspapers.

[The Free Dictionary]

Only 42 Folds To The Moon? Yes!

One of my students just can’t wrap his head around the power of exponents. Can you blame him? This week we learned that it would take just 27 folds of a piece of paper for the stack to reach the height of Mount Everest, and then just 15 more –a total of just 42 folds – to reach the moon! As we started the lesson, students guessed “one million” and “47 billion!” folds to reach the moon, so you can imagine the shock (and disbelief) in the actual number 42! Maybe the weirdest part is to think that it would take 41 of the folds to get just half-way to the moon and then just 1 more to make the second half of the journey.

[Scaffolded Math]

Other nouns that might work are pack, bundle.

As suggested by @jxh

continuous form paper

enter image description here

When used to print large continuous documents, they might not be split into separate sheets. By continuously folding two single sided printed sheets back-to-back and binding together a stack of continuous-feed paper along one of the folded edges, it is possible to flip through the stack like a book of double-sided printed pages. With this technique, the stack of papers is normally flipped top to bottom or bottom to top rather than side to side.


Another alternative is to consider the analogy of protein folding, the process by which proteins condense into their native 3D structure.

modeling of protein folding

Folding@home uses Markov state models, like the one diagrammed here, to model the possible shapes and folding pathways a protein can take as it condenses from its initial randomly coiled state (left) into its native 3D structure (right).


This suggests the word "structure", or as suggested by @ChrisH the terms "folded structure" or "resulting structure"



The arrangement of and relations between the parts or elements of something complex


Since you are considering coining a new term, how about

The result after applying one or more folding transforms.


folden + -ite


alternative past participle of fold





resident of, follower, product of


  • Consider illustrating with a picture of continuous form paper.
    – jxh
    Commented May 7, 2015 at 22:20
  • Some nice ideas here, I rather like "structure" though it would be better introduced as "folded structure"/"resulting structure" with subsequent references to "structure". "Structure" has meanings in many fields, so it may not be appropriate.
    – Chris H
    Commented May 8, 2015 at 8:39

Pleat? It comes from garment-making, and might be appropriate, specifically as it can refer to multiple folds.

definition from Oxford Dictionaries Online:

pleat /plēt/

noun 1. a double or multiple fold in a garment or other item made of cloth, held by stitching the top or side.
synonyms: fold, crease, gather, tuck, crimp; pucker

verb 1. fold into pleats.
"she was absently pleating her skirt between her fingers"
synonyms: fold, crease, gather, tuck, crimp; pucker

  • 1
    Due to a pathological desinterest in anything clothes-related, I may be mistaken here, but: Wouldn’t pleat suffer from the same problem as fold, namely being confusable with the point of a folding?
    – Wrzlprmft
    Commented May 7, 2015 at 10:38
  • Yeah, I kind of realized that after I wrote the answer, in that it is both a verb and a noun. Maybe just pluralize it, "folds"? Did you want a singular noun? It could be a thing, like the Ides of March. The Folds of May. Commented May 7, 2015 at 10:54
  • That may still refer to multiple points of folding or creases.
    – Wrzlprmft
    Commented May 7, 2015 at 10:58
  • I thought you only wanted to avoid referring to just one point of folding. I'm having trouble wrapping my head around the concept as it relates to mathematics, but to me, what you have pictured is a plural noun of multiple folds. Fold-field? Fold-zone? Folditude? Foldation? I like the idea of coming up for a new word for which there isn't one. Actually, foldation might be good in the same way foundation is the thing created when a settlement or what have you is founded. Commented May 7, 2015 at 11:34
  • Well, you can fold a piece of paper multiple times and still large parts of it are plain and without creases. Folds could still refer only to the creases instead of the entire, folded paper. — Foldation sounds good at first glance; you might turn that into an answer.
    – Wrzlprmft
    Commented May 7, 2015 at 12:34

Possibly the word you're looking for is sheaf. From TFDO:

sheaf n
2. A collection of items held or bound together

Usually this refers to separate objects bound together, but there is no reason it could not be used (or appropriated) for a set of folds.

  • 2
    As it happens, the word "sheaf" has one very widely-known use in mathematics (en.wikipedia.org/wiki/Sheaf_%28mathematics%29). Widely-known to professional mathematicians, that is. That doesn't mean it can't be used in mathematics with a different meaning, but it makes it a bit less attractive. Commented May 7, 2015 at 16:38

I know the term already has significant meaning as a mathematical term of art, and thus may be more confusing than helpful, but how about manifold? Or, the similar multifold or polyfold?

  • +1 Yes, it is the already established term: en.wikipedia.org/wiki/manifold or mathworld.wolfram.com/Manifold.html. A 2-D Manifold could also be called a surface. To the OP: you could also seek further clarify on Mathematics.SE
    – cobaltduck
    Commented May 7, 2015 at 14:50
  • 1
    @cobaltduck: What insights do you think Math.SE could provide me? If there are words in mathematical usage that I do not know, my readers aren’t likely to know them either. (I do know manifolds though and they describe something different or at least focus an a totally different aspect.) I am also pretty certain that no term has been established yet for what I want to coin here.
    – Wrzlprmft
    Commented May 8, 2015 at 8:54

I think "Pleat" has the disadvantage of ambiguity as to whether it refers to one fold or the complete object. A better fabric-related term would be "ruff".

Image from http://internetshakespeare.uvic.ca//Library/SLT/media/images/Ruff.JPG

enter image description here


There's several good suggestions already in answers and comments -- fanfold, fan, pleat -- (I think many of the rest will be unsuitable to a mathematical audience), and I think your own option of fold is also suitable. [Indeed, fanfold occurred to me before I spotted it in comments, and of those four I think it is slightly better.]

However, some more to chew on (in order of my preference):

  • pamphlet

  • fold-up/foldup

  • ruffle

  • corrugation

  • plication (the state of being folded)

  • Of those, I like ruffle best.
    – Chris H.
    Commented May 11, 2015 at 21:46

There's also foldout, which is "a folded leaf in a publication (as a book) that is larger in some dimension than the page" [M-W]. This is perhaps something that hints at previous folding that can be unfolded again. In analogy to that, one might think of a fold-in.

Getting inspiration from here, one might also think of typical objects that get folded, such as a map (not suitable, as already overloaded), or napkin.

  • Mad Magazine has a fold-in as a regular feature, and has since the 1960s. It is a picture that becomes a humorously different picture when folded in. Less than meets the eye? Commented May 7, 2015 at 11:22

Perhaps foldage, by analogy with (for example) 'coinage', something which is the result of the act 'to coin'.

  • Without source or quote, your answer would be better put as a comment.
    – P. O.
    Commented May 7, 2015 at 19:32
  • 1
    @P.Obertelli: Lack of sources and quotes does not make an answer belong in the comment domain; at worst it makes it a bad answer. But even this is not the case here, in my opinion. As this is a neologism (which I explicitly allowed), it cannot be backed-up with sources but only with argument and analogies, which the L. Guest did.
    – Wrzlprmft
    Commented May 8, 2015 at 9:00

The most logical answer would be your first choice which is "fold". To compare it to other mathematical operations: sum of two numbers results in a sum. product of two numbers gives you a product. sqr root of a number is still its sqr root.

  • Hi TheCutePup, welcome to ELU! With these suggestions, I think these are circular definitions; they do not describe the action taken to get there. The addition of (or adding) two numbers results in a sum; the subtraction of two numbers is a difference; the multiplication of two numbers is a product; etc. Square root might be okay, but an actual mathematician may have the verb associated with this.
    – Erich
    Commented May 7, 2015 at 23:58
  • 1
    @erich: Square root might be okay, but an actual mathematician may have the verb associated with this. – Yepp, square roots are extracted.
    – Wrzlprmft
    Commented May 8, 2015 at 9:04

If I were you and I really want to coin a new word morphologically related to fold, I would call it foldington, a neologism in analogy to single → singleton.

Or foldology defined in the sentence

Each choice of fold sets for a space is a foldology.

wherein space refers to the entire entity, and a fold set refers to some combination of existing folds (or some mathematical objects essential for the definition of isomorphisms between foldingtons). This is similar to the definition of topology in terms of open sets.

If you will, you can even call the entire object a foldological space.

A foldington is a foldological space containing a set X together with a foldology, Fx, consisting of fold sets made up of folds.

There exists an isomorphism between foldingtons (X,Fx) and (Y,Fy) if and only if there exists a bijective function between X and Y that preserves the foldology.


Capital 'F', Foldling. Sort of like foundlings; capitalizing it would make it unambiguously a name and not a term. And it'd be harder to miss that 'L' slipped in there.

  • Mm, or foldlet, or foldment.
    – hBy2Py
    Commented May 7, 2015 at 23:14
  • @hBy2Py - Foldlet is cute. Commented Dec 9, 2016 at 5:31

enfolding / infolding, n.

According to the OED, as well as being the action of the verb enfold, it can also be used as a concrete noun referring to the folds themselves.

So the result of the process of folding is an enfolding.

  • But then an enfolding is also the result of the process of enfolding and we have a disambiguity again.
    – Wrzlprmft
    Commented May 8, 2015 at 9:06

Superfold is a word that already exists and even means a grouping of folds. It does pertain to the world of proteins, but could easily be pressed into service here.

Noun: superfold (plural superfolds)

  1. (biochemistry) A large grouping of protein fold conformations

Source: Wiktionary

If you particularly wanted a neologism then I think you could combine the prefix Supra- with "fold" to make Suprafold. However I think that fails your basic test of unambiguity, or at least may not be easily understood by the majority...


a scrunch (from the verb, v.t., 2. to contract; squeeze together: I scrunched my shoulders. the free dictionary)



noun 2. the way in which constituent parts are interrelated or arranged.

source: http://www.oxforddictionaries.com/us/definition/american_english/topology


if you take a flat input and subject it to a specific series of folds, it results in a specific topology.

this definition suffers from the ambiguity between "the way" meaning "method" or "strategy" like "the way you dance" vs "the way" meaning the resulting style like "the way your head is attached to your body". but i think the distinction would always be clear from context.

for example: this sentence uses "topology" to describe the folding strategy:

random topology results in asymmetric shapes

this sentence uses "topology" to describe the resulting shape:

random folding results in asymmetric topology

come to think of it, you could just use the word "shape" :)

  • 1
    Apart from being already used in mathematics, the problem here is that topology refers to the way something is arranged and not actual result. The difference between topology and what I am looking for is similar to the one between typography and text, design and product or knitting pattern and scarf.
    – Wrzlprmft
    Commented May 7, 2015 at 17:34
  • i have updated my answer in an attempt to address your concern. i would expect that in your paper the meaning of "topology" would be clear from context. Commented May 7, 2015 at 18:02
  • Please don't forget to add attributions in plain text (preferably with a link) for your quotes.
    – Andrew Leach
    Commented May 9, 2015 at 11:08
  • i added an attribution to the definition and removed the quotation marks from the example sentences to clarify that they were not quotes. sorry about that. i am new here :) Commented May 9, 2015 at 13:25

I am recommending "Stack". While "Topology" may be mathematically accurate the term names a whole branch of mathematics and as such it names the item without adding to the explanation. The term "Pleat" is better but as stated points to the folds more than the interior of the result.

If you block off the view of the creases on each side then a stack or pile is what remains. Stack refers to the plurality of material at hand without a hint of how the elements came to be there, whether a nearby fold or a distant separating source.


The reference to continuous paper (who remembers dot-matrix printing?) suggests "fanfold", since it was often referred to as "fanfold paper".

Alternatively, "foldoid". It just sounds kind of neat.


Since you speak of folding, there is a well-known pattern in mathematics called the Dragon Curve. Imagine a long strip of paper successively folded in half, each fold towards the right. Unfolding such that each fold becomes a 90-degree angle, a very beautiful pattern emerges as the number of folds increases.

Dragon Curve recursively generated Image credit: Guillaume Jacquenot / Wikimedia

Folding always to the right results in a sequence of folds; for instance, folding three times results in the sequence RRLRRLL if you traverse the edge of the paper. Other fold patterns will produce alternate sequences.


A particular order in which related things follow each other

This works well in a generic sense, as your folded object may not always resemble the LRLR fold pattern of continuous form paper.


Brian Hitchcock's argument for "folded argument", coupled with OP's response that he's looking for a single word, arguably make the case for a neologism: foldob. I think OP should run it by one or two other people in mathematics that have the same specialty, tell them he's thinking of putting this in a paper, and asking them what they think of it. Similar to "pixel" (picture element), sometimes you just need a new word.

One benefit of this is that if it doesn't "catch on" (that is, if it doesn't become the standard way to refer to this in your specialty), it's still similar enough to "folded object" that (as long as you define it in the first use and explain that it means "folded object") any reader will always know exactly what you mean (because it's easily traced back mentally to it's origin).

It has the quality of being derived from "fold" that you wanted, it's a single word, it's very unambiguous. I say that you should just take the plunge and do it. If someone is reading your paper ten years from now and "foldob" has not become standard, it will still be trivially easy for them to understand what you meant.



"In mathematics, specifically, in topology, a surface is a two-dimensional, topological manifold."

source: http://en.wikipedia.org/wiki/Surface

this term seems to be used in the context of mathematics to capture very closely what you are describing. although it could also be used to describe 2d manifolds that are curved in 3d space rather than folded, i do not think that would distract from the subject of your paper.


I do origami. The words I encounter most often for the finished product, resulting from a sequence of folds, are

  • model

  • fold, which I believe you already rejected, and

  • finished fold

When the finished product is intended to look like something in particular, or to be used for a purpose, you can call it the name of the thing you are modeling or building, for example, boat, man in canoe, candy box, whale, toy, lampshade, tesselation, etc. Tesselations are nice because you have a sequence of repeated, complex folds that give you repeated patterns that create optical illusions.

You could also call it a

  • folded object or shape

There are special names for the intermediate results of a sequence of steps, such as pleat, accordion, accordion fold, sink fold, mountain fold, inside-reverse fold, swirl, pentagon, hexagon, preliminary fold, five-sided square, etc.

If each step is similar to the previous, you could call the finished product an

  • iterative fold

Your diagram looks like a

  • snaking fold

I suspect that you are talking about folding as a metaphor in a mathematical context, and that no tangible paper or other material is actually getting folded or creased. In this case, I think enfolding or folding in upon itself might be better than folding to describe the process, i.e. the mathematical manipulations that you feel are analogous to the folding of paper.

In case it's helpful: Note that in the process of doing origami, there are of course many steps that result in the model becoming smaller, but there are also steps that involve it getting bigger, e.g. pull out paper around the beak, unfold to step n, etc.

In Spanish, origami is referred to as papiroflexia, and the end products are called figuras de papiroflexia. Based on this, you could consider flexion (action of being bent).

Additional ideas: enfolding (for the process), enfoldment (for the end product), smocking (this is a special kind of embroidery done on top of pleated cloth), gathering (also for cloth, this is less precise than pleating), ruffle (the result of gathering a cloth strip), compactment (if the result of your folds is to make something much smaller and denser), layering, construction, sequence of folds, fold sequence, and coaxing (coax as in persuade, because you coax the paper into the desired shape), design, finished design, build, construction.

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