The Forgotten Flexagon - Numberphile

[@incription]

Weird flexagon, but ok

[@r-prime]

Weird flex, but ok

[@rawovunlapin8201]

@@B----------------------------D :o

[@kiverismusic]

Hhhahahahahahahahahah

[@VeritasQuasitor]

👏👏👏👏

[@KINGLADUDU]

It's a Parker flexagon

[@ryPish]

Ah yes, the slightly less magnificent *Parker Flexagon*

[@Sam_on_YouTube]

It is also square. And, as explained in the second video, the diagram doesn't work as well as it looks like it should. That makes this the Parker Square Flexagon.

[@LordHonkInc]

I love that even after three years that meme's still going strong

[@ABurntMuffin]

sonofabitch beat me to it

[@G.Aaron.Fisher]

@@LordHonkInc I finally bought the t-shirt. No regrets.

[@Klaevin]

@@Sam_on_KZbin it's only been 3 years?

[@Sam_on_YouTube]

My 8 year old twin girls love ViHart's hexaflexagons. I often help them make them out of straw wrappers at restaurants. Thursdays are half days at their school. You just gave them an afternoon project. Thank you.

[@duckrutt]

I use wrappers to make jumping frogs. The game is to land it in someones drink (preferably someone at your table but I don't judge) while not launching it somewhere it would be socially awkward to retrieve.

[@mvl71]

Thank you for directing me to hexaflexagon madness. I'll finish my current affairs and retreat to my room where I will happily waste away, folding hexaflexagons like there's no tomorrow. Gollum 2.0: my hexioussss

[@dragoncurveenthusiast]

Can you provide links to crease patterns for the jumping frog?

[@BloodyHaemorrhoids83]

I found a way to edit the sides on a hexaflreagon without ungluing it! me and my friends did a study on them a few years ago on top of the normal typically found studies, focusing particularly on editing. there are editing states with certain numbers of holes that determine the availability of editing and more. i’ve tried to bring light to this but most things about flexagons are multiple years old.

[@kimberlypichardo6884]

I think I've seen u on comment on ViHarts channel

[@Koisheep]

I was about to say "where my monomonoflexagons at" until I realised That's a Möbius strip

[@electromorphous]

*Duuuuudddeee!* STOP BLOWING OUR MINDS LIKE THAT!!

[@bbgun061]

And a plain sheet of paper is a bitetraflexagon.

[@muchozolf]

@@bbgun061 or bi-n-flexagon, it can have any number of sides.

[@zmaj12321]

duuuude

[@1DerSiedler]

@@muchozolf Than it's no longer a sheet, at least I wouldn't call it so.

[@OrangeC7]

Doodlephile is just Vi Hart's channel

[@brianmiller1077]

and 12Tone is doodlephile with elephants

[@GrapefruitGecko]

Haha this is so true

[@want-diversecontent3887]

Sem Zem is Vi Hart minus the Doodlephile

[@liquidkey8204]

I mean yes, but like yes.

[@shim64]

and my channel is doodlephile without the math

[@wishiwasabear]

*And to make it, we are going to use a square-* Oh, here we go again.

[@ejnissley546]

Kuma You got an issue with that?

[@CasualMitosisCollective]

@@ejnissley546 nope. Just a Parker square flashback.

[@OsyenVyeter]

It can be a rectangle. I have one made of playing cards.

[@seeseefok7659]

ah sh** here we go again

[@Triantalex]

??.

[@mrmonster3434]

"You could draw pictures - I'm not very creative, I used numbers. This is NUMBERphile, not Doodlephile!" 70 seconds later... "We're gonna use colours, cos that's how we roll."

[@OrangeC7]

To be fair, Doodlephile is kinda what Vi Hart's channel is for

[@jones1618]

"Dammit, Jim. I'm a doctor, not a bricklayer!"

[@woodfur00]

I loved how defensive he got about that

[@NortheastGamer]

And then proceeds to not use those colors, or the circle on the flexagon at all for the whole demonstration.

[@lyrimetacurl0]

That would be colourphile.

[@awsomeabacus9674]

I generally don't like pick up lines, but "You wanna see some new flexagons" is definitely a winner.

[@mcnichollsdj]

I wanna get flexagons with you... - sorry, didn't mean it to sound creepy!

[@radguitar1]

Matt: * Uses white paper * Brady: * Struggles with white/balance for most of video *

[@WTFAnimatonsHD]

Hi

[@crobodile]

hi

[@cuboembaralhado8294]

Hi

[@griffinshorts785]

Hi

[@batulkarim1482]

Hi

[@rytas]

I appreciate how you randomly got odds on one side and evens on the other.

[@OrangeC7]

_Cool coincidence_ or *freaky parker conspiracy?*

[@shim64]

😨

[@Triantalex]

??.

[@GraemeMcRae]

Very nice! My granddaughter (age 7) and I made two flexagons and colored them in. The project is complex enough to be entertaining, but simple enough to stay within our attention span.

[@_sine_]

The only time where "weird flex but okay" is valid

[@LeoStaley]

Numberphile: forgotten flexagon Vihart has joined the chat.

[@SuperAWaC]

@@tthung8668 it's funny how easy it is to get even very high end mathy types with party tricks

[@liquidkey8204]

@@SuperAWaC Yeah

[@Triantalex]

??.

[@Watchmedothatfor.u]

​@@Triantalex vi hart is a math channel , if you don't know of course .

[@error.418]

If you've watched Vi Hart, then you know you don't need glue to make a hexaflexagon. There are folding methods to do it.

[@BloodyHaemorrhoids83]

I found a way to edit the sides on a hexaflreagon without ungluing it! me and my friends did a study on them a few years ago on top of the normal typically found studies, focusing particularly on editing. there are editing states with certain numbers of holes that determine the availability of editing and more. i’ve tried to bring light to this but most things about flexagons are multiple years old.

[@Triantalex]

??.

[@Watchmedothatfor.u]

After vi hart I didn't even watch till the end :(

[@modernkennnern]

Not gonna lie. I thought this was a Vihart video when I read the title. Had to recheck the channel name

[@TheLostSorcerer]

@Jack Could have been a colab.

[@cheyofhearts]

I literally jumped up thinking Vi uploaded 😂

[@ericstoverink6579]

It's a Parker ViHart video.

[@Triantalex]

??

[@maxhaibara8828]

next video will be "N-dimensional Tetraflexagon"

[@matthewellisor5835]

He IS the Kwisatz Tesseract!

[@murrfeeling]

All you gotta do is fold a cube.

[@KuraIthys]

In 4 dimensions, isn't this essentially what a hypercube amounts to? Let's assume you 'fold' a hypercube in on itself. Now all of it's constituent 3d cubes occupy the same 3d 'space' in some sense. If you were to navigate this space by somehow passing through the walls of each cube, you'd end up in another cube, and you can keep going through the same 'wall' 4 times in row before you appear at the opposite wall of the cube you started in. However, certain sequences of such moves put you in a different set of cubes from which you cannot navigate back to the original set by going in a single direction... Actually the graph of this Hexatetraflegagon in terms of which faces you can see simultaneously has a lot in common with what you'd see if you graphed a hypercube in terms of which other cubes you can reach by passing through the walls of the cube you're currently in...

[@JNCressey]

@@KuraIthys, When you fold a square, two of the edges lay on top of each-other (same 2D space), and the other two become folded in half on themselves, and a crease that looks like an edge joins the middles of the folded edges, and the final shape is a rectangle that's half the square. So my guess for folding 3D would be that a 'folded cube' would involve some (square) faces being lain into the same 3D space as each-other, and some (square) faces being folded in half on themselves (and we know what a folded square looks like), and a crease that looks like a square joins the middles of the folded faces, and the final shape is a cuboid that is half the cube. And my guess for folding 4D would be that a 'folded hyper-cube' would involve some (cube) cells being lain into the same 4D space as each-other and some (cube) cells being folded in half on themselves (and folded cubes are described in the first bit), and a crease that looks like a cube joins the middles of the folded faces, and the final shape is a hyper-cuboid that is half the hyper-cube. But that's just a guess. Is there any math that says it behaves differently? Perhaps shapes with more dimensions than 2 are just completely rigid and can't be folded? Also there's different ways to fold a square in half. The half rectangle way, the triangle way, and some random oblique angle. So maybe something that sounds completely different is equivalent.

[@MrEugenio1994]

Do you even N-flex, bro?

[@N.I.R.A.T.I.A.S.]

5:18 "It's Numberphile. It's not Doodlephile, is it?" Brady. *Start a channel called Doodlephile.*

[@SimonBuchanNz]

Isn't that Drawfee?

[@brianlane723]

Just use Hovah to register the domain.

[@KingJellyfishII]

No that's vi heart

[@pvic6959]

@@KingJellyfishII i support this message

[@syriuszb8611]

0:24 "Fold it in half, witch ever way you want" Are you sure?? Well then, I want to fold it in half diagonally!

[@rewrose2838]

Does it work? A triangular flexagon maybe?

[@colscoco6616]

Yeah, if you look at 4:35, #1 and 2 are the only numbers not to be in any corners (I think)

[@johnchessant3012]

I liked this video because it encapsulates the spirit of doing maths especially well. It's all about experimenting where we don't know at the outset what we'll find, or whether it'll even be interesting, yet here we are, appreciating Matt's tetraflexagon graph. Of course, other Numberphile videos are like this, too, but the spirit of experimentation comes across most clearly in this one.

[@theunknown4834]

When your origami skills actually became useful Oh wait there's veritasium

[@B3Band]

It's not origami if you use scissors.

[@xario2007]

Also, flexagons are only "useful".

[@liv9589]

@@palmomki one of the latest veritasium videos is about origami and it's useful applications in engineering

[@error.418]

@@B3Band Kirigami

[@OrangeC7]

@@B3Band You (technically) don't need scissors to make a tetraflexagon. You could (theoretically) take a long strip of paper and fold it in such a way that the ends are connected, and then from there it's (almost as if) it were cut in the middle

[@PTNLemay]

Aww, I thought it was going to be a collab with Vihart.

[@LaGuerre19]

Fantastic forgotten finite fractal flexagons freely folded for fun! Fie, foursquare fingerwork! (Nice work, Matt and Brady!)

[@steveydoesglasgow]

Love the commitment to making tiny flexagons at the end, shout-out to whoever managed that!

[@DanTheStripe]

0:20 You're going to use a square of paper, are you, Mr. Parker? A square? Parker? Hmmmm....

[@bashily2844]

Parker chose option 2 when someone told him to be there or be square

[@OsyenVyeter]

It’s ok it can be rectangles. I have on made of playing cards

[@Triantalex]

??

[@wendysolomon1608]

at the behest of one of my favorite students, we once embarked upon a quest to create a dodecahexaflexagon. It works, but is quite fussy and fragile. Even graphed it out! Love them!

[@EdoTimmermans]

Thanks to your comment I just found a KZbin video on how to make an icositetrahexaflexagon named 'Awesome!! 24 sided hexaflexagon!'.

[@ffggddss]

Several decades ago I actually made a 48-faced hexaflexagon. The finished product was veeeeerrrry clumsy to operate! Fred

[@laurihei]

"And to make it ...we're gonna use a square of paper." Ok, queue up the memes then. It's not like we were only 20 seconds into the video already.

[@laurihei]

This must either be the record or at least getting close.

[@Fra321]

@@laurihei A parker square of a record attempt.

[@Triantalex]

??

[@laurihei]

​@@TriantalexParker Square 😅

[@rohanglenmartin]

That was fantastic! You've inspired me to use this to make a treasure map and build a D&D campaign around it.

[@Dixavd]

When I was at school about a decade ago I remember kids in class making these Tetraflexagons whereas I hadn't heard of a hexaflexagon until today. They'd play games similar to that octahedron papercraft you put your fingers in: for instance, they might start on a given arrangement with the names of other kids on and say "fold it 3 times and that's the person you'll marry".

[@xenialafleur]

We played with these all the time with these in school.

[@charlenejo2490]

You mean what was called a “cootie catcher?”

[@the_mad_ratter]

I had totally forgotten about these until I saw this video... my dad had (and I now have somewhere) a couple of display "toys" from the 70s that did this, about the size of credit cards (but much thicker and made of plastic) the design on one side had a series of linked circles (like the olympic logo), and the other side had them all separated.

[@pherlong7]

Rubix magic?

[@TforThought]

It is wonderful that a bunch of numbers/symbols and what we can do with them. Can even explain things like rubrics cube, Hexaflexigon etc

[@HrsHJ]

So Parker Square guy is back what's next?? Maybe bring back everyone's favourite James Grime??

[@lazarusnecrosis5869]

I love Matt and James both. It's hard to choose a favorite.

[@lr31415]

YES PLEASE

[@vanderengland5775]

I’ve been up to 24 faces with a hexaflexagon. It’s wild. Also I’d love to know how to make a tetraflexagon with more than 6 faces

[@adamweishaupt3733]

Don't each of the faces have 3 potential "partners," the one that reveals them and the ones that come after a horizontal and vertical fold? Why aren't those represented in the graph? Everything except 1 and 2 is only listed twice.

[@absalomdraconis]

The "center pair" has 4 neighboring pairs, two for each fold direction, but the other pairs only have 1 on each axis. In particular, to get to anything else you would have to unfold the flexagon into a flat sheet again. This is why you see him trying to fold it in certain directions before giving up on occasion: this flexagon does _not_ allow infinite folds along a single axis.

[@fireballme1153]

You can also flip to the other side

[@highpath4776]

Think about the start shape, it has 4 corners, those corners match with two numbers on each side of them, those numbers have only one additional number they match to this explains how a starting shape as folded has the number of axis combinations and with what.

[@wafikiri_]

This tetraflexagon has a two-square map. Once I mapped a hexaflexagon and got a central triangle touching three other triangles with its three vertices.

[@MarcusAntonio.]

"You wana see some new flexagons?"" i'm goin, "YEESS." 12:21

[@yerwol]

It's like you imagine some guy with a long trenchcoat in the street approach you, opening up one half to reveal a vast array of flexagons pinned to the inside. The seedy underground world of flexagons

[@guhan4606]

Weird flex, but Parker square

[@TheRealGuywithoutaMustache]

I'm gonna "flexagon" people who don't know what a flexagon is

[@Jitatman]

Just Some Guy without a Mustache im seeing you everywhere in the comments

[@matthewellisor5835]

Some Guy, it that a form of jiu jitsu? You know, folding clothes with people still inside?

[@narusferree6506]

Weird flex, but okay.

[@sachiel197]

@@matthewellisor5835 I think you mean involuntary yoga

[@Abdega]

Top 10 anime flex(agon)s

[@wafikiri_]

I used to make hexaflexagons, especially for children. I never attempted the hexakisoctahexaflexagon, for you would need a really robust strip (steel recommended, with hinges, anything under 4 ft as side length would be too bulky) just to have 6x8=48 faces.... Rumor has it that one tried to make one, but his tie got trapped in it and when he flexed the hexakisoctahexaflexagon to loosen the tie, he himself got trapped and nobody has heard from him since....

[@AchuthanKarnnan]

😶

[@atticuskoch2965]

This is the first video I've seen from this channel and it's really cool. I wanna see more of this guy making squares

[@qwertyTRiG]

Matt Parker's boundless enthusiasm is a delight. May I also suggest the Festival of the Spoken Nerd?

[@Mikk84]

We did our Wedding Invitations with a card like this, so the people had to "find" the date and location. Had a few people calling us, because they didn't found the right page xD

[@TheSequentCalculus]

"Someone called Vihart"? That's an insult, you should address the Queen of Tau properly.

[@akudumb3021]

Max Maria Wacholder Exactly. Shame on his cow!

[@Qenton]

Wow, I didn't know that one! I always made the one with the same number of squares but outer corner squares are removed and an X in the center. You can fold it in one motion. This one only reveals 4 faces of the 6 but does cycle nicely. I guess you would call it a quad-tetra-flexagon? I did make a Dodeca-hexa-flexagon once in the 80s but had to figure that one out myself.

[@1p6Gaming]

And by using a pattern like so, you can make a five sided tetraflexagon, a pentatetraflexagon! (o's are paper and slashes are cut out squares) ooo/ o/oo oo/o /ooo

[@digitig]

I learned about flexagons from Martin Gardner's Mathematical Puzzles and Diversions books back in the 1960s. I got as far as making a dodecahexaflexagon. I also learned the Tuckerman Traverse, a systematic way of getting to all the faces on any flexagon.

[@robinbrowne5419]

Thanks.That's great. I showed this video to my little grand daughter and now she's busy trying to make a flexagon. However she doesn't quite get it yet. She is just coloring squares on the paper. She will probably need a bit of help from grampa. But a really fun activity for kids. :-)

[@maehmaehmaeh9560]

Cool video! After watching I sat doen and created a 14-faced tetraflexagon, although it's a bit hard to fold and theres some ugly folds to go from one dtate to another.

[@Adam-zt4cn]

9:37 I'm pretty sure that diagram is incomplete. It's missing 4/3 at the bottom and 6/5 on the top. Then, the entire graph would be symmetric for all the numbers.

[@brettbreet]

It seems that there should be 3 combinations for each side. So if {1: [2,3,5], 2:[1,4,6]...} then the other sides 3, 4, 5, 6 should also have 3 "pairings" each. I imagine this object is symmetrical and no side is "special" :)

[@rmsgrey]

@@brettbreet Your imagination has failed you. The net has 8 corner facelets and 16 edge facelets that will behave differently in the final structure, and there's no way to distribute those 24 facelets among the 6 faces of the finished flexagon so that they each have 1 and 1/3 corner facelets and 2 and 2/3 edge facelets...

[@brettbreet]

@@rmsgrey Ah, I see that now. Thanks for the explanation!

[@davidmoore1253]

@@rmsgrey I was wondering about this too. Thanks!

[@ezrastewart543]

Uhh... 2+2 is 4?

[@ditzfough]

Can we just appreciate the fact that we have Matt Parker on Numberphile mentioning Vihart. I love when my youtube nerds talk about and learn from each other.

[@Marcara081]

"You can do anything in one cut so long as you're clever about how you fold it." Feels like that's related to the Inscribed Square problem.

[@dropintheocean7779]

*The best thing about this channel is that it contains so many languages that anyone understands what is said in the video, especially Arabic*

[@amoryacosta2915]

You can also make a dodecahexaflexagon. My friend and I worked on it for almost a whole semester before getting one to work properly.

[@sandervanderhorst9851]

1:40 "you can get rid of those"?!? Nooo, make another one!

[@fiziwig]

I remember hexaflexagons from Martin Gardner's Mathematical Recreations column in Scientific American. That's been a long, long time ago.

[@BunniBuu]

This came out today and yet I was getting recommended Vihart's hexaflexagon videos all yesterday. That's some interesting algorithm, KZbin

[@Yevgen4000]

"There are 3 easy steps and one difficult step" Me, an origami master: *ARE YOU CHALLENGING ME*

[@lasamisalagne7377]

I'm gonna flex in my maths class with my newly aquired knowledge about flexagons

[@XenoghostTV]

"flex" is an understatement hahahahah

[@MrMidlandman]

Flexagons are at least 50 years old! Check out 1970's books on Recreational Maths by Martin Gardner, (though probably out of print now!)

[@WDCallahan]

I was immediately wondering why 1 and 2 have three states, but the rest only have two? These are things I noted: The ones and twos are separated on the unfolded paper. Everything else is in pairs. All even numbers are on one side, and odd numbers are on the other. Numbers with only two states take up corners and edges. Numbers with three states only take up edges. All two state numbers are written in the same orientation, whereas I can see half the 2s are upside down. Presumably two of the 1s are also upside down, but it's not possible to tell. I want to know how it an fits together!

[@senthilkumaran5255]

@CGPGrey Hexagons vs Flexagons who wins?

[@ffggddss]

The full name of this beast is the "hexatetraflexagon." It's the 6-faced member of the tetraflexagon family. And just like that other family, the hexaflexagons, the simplest (non-trivial) member has 3 faces - the tritetraflexagon. And like the 'hexes', the 'tetras' were introduced by Martin Gardner in his monthly column, _Mathematical Games,_ in Scientific American. The introduction of the hexas was his first such column, actually an article titled "Hexaflexagons," in the Dec. 1956 issue, the popularity of which launched the Mathematical Games column from then on, for a couple decades or so. If my reckoning is correct, the tetraflexagon article must have been in May 1958. That column has instructions for making a tri-, a tetra-, and this hexatetraflexagon. However, the 6-faced one is shown there to use a cut, several folds, and a spot of adhesive tape; Matt has more elegantly shown us a cut-free construction. Thanks for that, Matt, and for helping us all maintain our flex-ability! BTW, the diagram Matt is attempting to construct for the 6-4-flex is akin to what Mr. Gardner goes into in his Hex article, for which the diagram is (or shows how to execute) a Tuckerman traverse. So is this now a Parker traverse? Another point of interest: The inventor of the hexaflexagons, Arthur Stone, and 3 grad-student colleagues worked out the ins & outs of the things starting in fall 1939. One of those grad students was Richard Feynman. Stone also invented the tetraflexagons, although the basic structure of the tritetraflexagon dates back at least to the 1890's, in a toy called "Jacob's Ladder." *Sources:* _The Scientific American Book of Puzzles & Diversions,_ pp 1-14 _The 2nd Scientific American Book of Puzzles & Diversions,_ pp 24-31 Fred

[@007bistromath]

I'm looking at a KZbin comment with citations. I have fallen into a very strange parallel dimension.

[@pmcpartlan]

It was 1956, check the second video...

[@ffggddss]

@@pmcpartlan Yes, as I said, the 'popular' introduction of hexaflexagons was in the December 1956 issue of SciAm. The introduction of tetraflexagons, however, was over a year later. But both were invented in or shortly after 1939, by Arthur H. Stone. Fred

[@gudadada]

So simple and complex at the same time.

[@piotrmecht2500]

I remember this flexagon from my chilhood. You could find it as a promotional item in some crisp packages (brand owned by frito-lay). It used images instead of numbers

[@c4oufi]

When I was into flexagons, I got bored of hexa-hexa-flexagons, so I made a dodeca-hexa-flexagon. I ended up making myself a Feynman diagram and man, was it a tough one.

[@dougr.2398]

Václav Coufal there are too many bubble diagrams involved

[@kevinmartin7760]

It bothers me that the hexaflexagons must be glued for assembly but the hexatetraflexagon does not. It also bothers me that the 1/2 configuration can be transformed to four other configurations, while all the others can only transform to two. The operations from 1/2 are the combinations of the choice of which face to close (hide) and whether you close it vertically or horizontally. From the other configurations you still get a choice of which face to close, but (I assume) one way of closing each face cannot be opened in a manner different than it was closed. The closed configurations represent the arcs on your chart; perhaps you could follow up with a chart identifying the arcs and showing these dead-end arcs.

[@frankhooper7871]

I was taught how to make both hexaflexagons and tetraflexagons in my highschool geometry class in 1966/67 🤓

[@justsomeone4347]

Vihart: how dare you fight my hexaflexa-skills

[@Watchmedothatfor.u]

OK. I'm late with the answer ) stopping . me : I should get out * watching vi hart *

[@C4pungMaster]

If anyone is interested, there are a whole family of flexagons made by Scott Sherman (same youtube channel name). Some of them are puzzles and he post the diagram on his website. I had alot of fun years ago with them

[@jonathanrobinson8926]

Can you make a Flexagon with all combinations possible other than the obvious sheet of paper? If so, is there a pattern to the numbers of flexagon in which it is possible?

[@chriscraven9572]

I was given a wedding congratulations card in the form of a hexatetraflexagon last weekend. Brought back fond memories of Martin Gardner's articles and books.

[@munjee2]

5:56 I had the exact same thought when I passed the video at the start after Matt showed how to make it and played around with it for an hour

[@gabrieldoudna6570]

this is the most satisfying numberphile video in a while

[@rat_king-]

Missed the last two combos of 5/3 and 4/6. but what can i say when something acts like a 2d object behaving like a 3d number of edges what do you expect? Might want to go through and check that...

[@duopenottihihi]

Show this to vihart

[@justinhoffman5339]

The video introduced me to "a section, long ways" aka The Parker Column.

[@darthalex314]

I made a hexatetraflexagon after reading your book three years ago... I still play with it occasionally.

[@MusicCriticDuh]

I'm pretty sure that ViHart hadn't forgotten about the beloved,hexaflexagon!

[@gustavgnoettgen]

The one wanted to be a cube. The other triangular. Together they fight for their destiny. *_FLEXAGONS._* Now on VHS and DVD.

[@skfok8472]

1:26 and that's how you make a nether portal

[@ionobelisk]

Back in the '60s, ICL (British computer giant of the time) had promotional items that came in the form of a garishly printed A4(?) Sheet of thin card and instructions to cut it into strips that had marked triangles that you could fold into a splendid hexahexaflexagon. I wish I still had mine: it was an object of kitsch psychedelic beauty. One wonders if any still exist.

[@BlessedForever888]

I love the fractal flexagons at the end - super adorable

[@ivantheczar]

I learnt this version of square flexagon back in an education TV program some 30 years ago XD

[@ScottyUtHome]

Instead of that diamond shape drawing, you.could have drawn the lines horizontally & vertically as a map for which fold gets you to the next number combo.

[@unknown_demi6902]

someone get vihart on the phone, we got fractal flexagons.

[@PalladianPD]

I once made a dodeca-hexaflexagon. It was super cool but it was a lot of work and slightly complex.

[@royschreiber1]

I thought this was going to be a collaboration with vihart, but this was also great

[@sander_bouwhuis]

I would simply create a transition matrix. The nice thing about that, is that for a transition matrix M you can do M^n to determine where you can get to in n steps.

[@oxXBubbleXxo]

Had one from Mc-Donalds from back in the days... loved to fiddle with it

[@mychairmadeafartnois]

Some time in the mid 2000s I got a flexagon out of a package of something. I think it was string cheese. I’m pretty sure it was spongebob themed. It must have been this sort of flexagon because it was a square. I spent a lot of time mesmerized by it. Thanks for reminding me about that, this was great.

[@shreerangvaidya9264]

If you fail making any flexagon, you mostly get a Möbius strip, or as you can call it, a (mono)monoflexagon.

[@Emma-rw8yo]

Can we take a moment to appreciate the person who made all these flexagons for this video

[@s1ddh4r7h.p]

This is such a throwback to his old book lol

[@tiavor]

I remember this one, I made one of those when I was very young.

[@thatbozobri]

dang they real called vihart here

[@rossradtke]

Behind Matt on the shelf is a (yellow) cube passing through itself (purple)... just like reading a book series a second time you notice all the things to come hiding in plain sight.

[@MrConverse]

If you renumber the 1s 2s and the 2s 1s then the evens all run together and the odds perpendicular in Matt’s graph.

[@Pulsar77]

A better numbering scheme would be (using Matt's colours at 9:38): 1: orange, 2: cyan, 3: blue, 4: magenta, 5: red, 6: green. This way, the sum of each opposite pair is a unique number between 4 and 10: 3+1, 5+1, 3+2, 5+2, 6+2, 5+4, 6+4.

[@XeLaNoiD]

When you start calling your paper square a Parker square.

[@unvergebeneid]

How very bold of Parker to do a video on a _square_ shaped flexagon, made from a _square_ piece of paper. He _must've_ known what the comments would look like.

[@MurrRockstroh]

First time I saw one of these was when I got the board game Keyper by Richard Breese that came out in 2017.

[@angelaphsiao]

Highkey hoping you and Vihart collabed on this

[@themadhattress5008]

Definitely waiting for ViHart to make a reaction to this video now. Unfortunately, I'm going to have to wait a while.

[@andymcl92]

I'm not that creative a person, so I was quite pleased with myself when I made my girlfriend a tri-tetra-flexagon gift with 4 pictures of us on it (two 2*2 square pictures of us and two 1*2 portrait pictures, one each). She's now my wife, so apparently she was similarly pleased! :)

[@woodfur00]

Wait wait wait. A tri-tetraflexagon? And you're not gonna tell us how?

[@andymcl92]

@@woodfur00 From memory!: The net is 6 squares connected like this: XXX XXX Fold the left two in top row over the front of the third and the right one the bottom row round the back of the second to get something like: (X)X X(X) (Where the brackets mean it's two layers thick.) Then you need to stick the two "ends" from the original net together. If you want to make this easier, you can start with a net of: XXX x XXX Where the x is just a flap. When you're done, sides 1 and 3 are like the inside of a book, and 2 is the cover. Which side of the book you use as the spine determines if you see 1 or 3. The sneaky thing is that 1 and 3 always appear the same, but 2 will be either of: 2a2b or 2b2a 2c2d 2d2c depending on if 1 or 3 is showing. It's basically two 3*1 pieces of paper folded in to z shapes and glued on top of each other, but one of the zs goes in the opposite orientation :)

[@bordershader]

@@andymcl92 thanks for the effort you put into explaining that 😊

[@andymcl92]

@@bordershader Ach, I find the more I explain things, the better I understand them :)