Can I Solve This Unsolved Math Problem?

[@MrAdBounty]

Finding a list of number from a random email chain from 30 years ago that answer exactly a very niche math problem is peak internet

[@andr101]

Ahah, true

[@hiphyro]

pick internet

[@themultiverse5447]

The internet 30 years ago LOL

[@stanstrum]

@@themultiverse5447 By '95, there were already ~25,000 websites. That's 30 years ago lol.

[@Iden_in_the_Rain]

@@themultiverse5447only 1994, before the 1990s that’d be close to impossible

[@Zosso-1618]

As sure as I am that you’ve been working on this for a good while, I still choose the believe the funnier option that you watched Vsauce’s short last night and obsessively solved the problem and edited this video in less than 24 hours.

[@dache85]

nice pfp

[@InsanePigeon]

I thought the exact same thing

[@circumplex9552]

hello zosso

[@Zcon18]

​@dache85kbity!!! (⁠つ⁠≧⁠▽⁠≦⁠)⁠つ

[@SchepInza]

that would be impossible

[@Fedor-n4y]

Hello! Last summer I explored this problem by myself, and (already known) results I got were published in the Crux Mathematicorum. The thing is that 12 faces is not the only possible case, because according to the formula i found, there could be 15,16,19,24,27.... faces with certain properties.

[@xynonners]

bump this guy

[@D---3]

what the name of the pub

[@yaminnew2953]

Could you share the title of your paper?

[@yaminnew2953]

Ah I found it. Its titled "Polyhedra with Every Face Connected to All Others Through Edges" by Fedor Pavlov.

[@Fedor-n4y]

@@yaminnew2953 Yes. Sorry i tried to reply to you, but it seems like i have some problems with youtube

[@crazzykai]

1:37 I seriously thought "why would you put light-blue and blue next to eachother its going to be so difficult to tell them apar- oh-"

[@FlummoxTheMagnificent]

What's the "oh" part? I don't understand.

[@harsinsinquin4032]

@@FlummoxTheMagnificentall faces are adjacent so it’s impossible for them not to touch

[@PeterNerlich]

@@FlummoxTheMagnificent The problem statement is finding a polyhedron where any given pair of faces always share an edge. So the almost-solution that was colored with dark- and light blue, among others, could by definition not have been colored in a way where light- and dark blue didn't touch anywhere. So it was really delightful reading @crazzykai's comment, getting confused by it because this problem is so mindbendingly difficult to grasp, and then finding out that the missing piece was literally the premise that started the project in the first place

[@lilyoy7942]

Lol I still don't get it can you explain? I mean they can't be the same face since it'd have to have a crease...

[@StefanReich]

@@lilyoy7942 Every face is next to each other face. That's the main property of this polyhedron. So light blue and dark blue will always touch

[@trinityy-7]

i would have solved so many unsolved problems if i just lived in a time before all the problems were solved

[@runekongstadlarsen7569]

so true king

[@StreetSurfersAlex]

I feel you. Our minds were made for simpler times to shine

[@Monkeymario.]

You mean time travel and bring today's knowledge with you?

[@markojojic6223]

So true. I feel like I would have probably been a decent asset in solving in most periods like that

[@EddieA907]

Lol Amen

[@addiboi123]

Very cool findings, but I would not be so quick to conclude that it is "very unlikely" that there isn't another solution out there. It's not too uncommon for us to make a conclusion about something because of overwhelming empirical evidence, only to later find a counterexample that disproves it. See Skewe's Number for an infamous example: (First counterexample was 10^316)

[@HighMarx]

Also: the recent counterexample to the fishbone conjecture!

[@moth.monster]

Okay then, go find a counterexample :)

[@psymar]

Also Fermat Numbers. Fermat found the first 5 were prime and conjectured all were prime but couldn't test further as they get big fast. Some decades later Euler proved the 6th was composite. So far, as far as we know, *only* the first five are prime; we've proven 326 others composite.

[@dl4698]

Yeah fr. Like I really loved this video and all the amazing work he did in it, but I can’t help but take a slight issue with the title and his claim at the end that it’s “probably” solved. Like that’s literally not how math works…… The Riemann hypothesis has been proven up til like some unfathomably large number, can we just say “yeah probably true” and call it a day then?

[@ffc1a28c7]

tbf, there are some inherent bounds on the solve state for this. You aren't trying to show it for every integer. You're showing it for a collection of vertices, which is fundamentally (though really large) bounded.

[@an_asp]

Seeing you struggle a little with that objective function makes me surprised you never looked into multiobjective optimization. It has a lot of advantages when you're trying to minimize or maximize multiple conflicting values, especially in maintaining diversity across your search landscape.

[@BTElectric]

MOO!

[@adrianantico3750]

Nevergrad in python...

[@JaredJeyaretnam]

This is why it’s great to make a video like this and make the code open-source - CodeParade never claims to be an expert in this and is never going to be able to consider every perspective, but the power of the community means that we get insights like this

[@BladeNgames]

This would be fine if we cared about the two values combined, but ideally only interesting shapes appear for values with one global minimum or the other, I would believe

[@_Epidemic_]

Lmao Vsauce just made a short that references this problem

[@_Epidemic_]

funny coincidence

[@bl4cksp1d3r]

Just thought about that as well lol

[@robbiekavanagh2802]

I thought I recognised the shape in the thumbnail!

[@B-fq7ff]

@@_Epidemic_ not a coincidence this guy watched the vsauce video

[@deltaradiation]

exactly why i know about it loll

[@happygimp0]

You didn't solve a problem, but you made a, probably new, conjecture. If you can prove that conjecture or disprove it, then you solved a mathematical problem.

[@lucbloom]

Exactly. “Did I solve it? Probably.” in math world means “a solid no.”

[@thomasrad5202]

Yes, unfortunately it is all too uncommon to share / publish incomplete findings. however, this is the best way to advance collective progress.

[@samuelthecamel]

Summoning Salt has become an artstyle

[@Tomkat53]

I also heard the theme music and thought... SUMMONING SALT!

[@steej]

bro really just dropped a new shape

[@Monkeymario.]

It already existed

[@misss.magdalene]

what the hell hi steej

[@steej]

@@Monkeymario. show me where it was.

[@zote_the_mighty]

​@@Monkeymario. Why must you withold this information from us?

[@greenberrygk]

@@zote_the_mightywell I mean it existed it just wasn’t discovered

[@cipherjoe9]

Love the Summoning Salt-inspired intro

[@DietermiGamzD125]

My thoughts exactly

[@fireballferret8146]

It's a free-to-use song (I forget what it's called) EDIT: not as free as I thought

[@felixherz2864]

@fireballferret8146 Home - We're finally landing

[@XEqualsPenguin]

They also use the same kind of graph that Summoning Salt uses!

[@bee_irl]

As well as the same song Wirtual uses, _En aften ved svanefossen_ (at 6:45)

[@optozorax_en]

Try CMA-ES optimization algorithm, I tested it against differential evolution, nelder-mead, particle swarm, even gradient descend (of my non-differentiable simulation), and it worked better than anything. Also, your loss is too discrete, it's hard to optimization algorithm to find anything good using it. Try to smoothining it, for example add some distance between something, that when minimized to zero, this removes one point from your discrete loss. If you implement this smoothing, you should just add to your current loss, that is, when you find 1 less intersection, your loss gets -1. I found that to be most effective for 0-th order optimization methods. Because when you have such discrete steps after finding it, algorithm will not forget it and will not trade this for some minor improvements in another place. I found this perform dramatically well in my experiments too.

[@loganwilson6282]

So funny to see you suggest CMA-ES, I’ve never seen anyone talk about it in the wild! I go to harvard and just took a class this past semester with the guy who invented it and he talked about it so much LOL… wasn’t sure if it was actually that cool or if he was full of himself. As I was watching I was thinking it would be perfect for this type of optimization!

[@optozorax_en]

@@loganwilson6282 lol, world is small. If you see that guy again - send him my best regards! And say him that I wait for CMA-ES-2 for discrete values :) I learned about CMA-ES from video "Flexible Muscle-Based Locomotion for Bipedal Creatures".

[@mrsillytacos]

Like this so it becomes the top comment.

[@hamiltonianpathondodecahed5236]

​@@loganwilson6282 Plot twist, OP is the discoverer of CMA-ES

[@goblinry]

Just started watching love the intro, cant wait until the twist where matt turk comes out of retirement and solves the problem right before you do.

[@moth.monster]

Unfortunately, Anti Code-Parade ran all the solvers backwards, so his attempts were nullified

[@veggiet2009]

Instead of the "pointy headed duck" you should call it the "gerrymander" 😂

[@quintopia]

why not "hat-on-a-hat" since apparently mathematicians are happy to call things "hat" that look nothing like hats.

[@Monkeymario.]

What's a gerrymander?

[@lukasjetu9776]

​@@Monkeymario. "gerrymander" are just jumbled up German words "gerry"-"man"-"der", we can rearrange them to "der"-"gerry"-"man" and get the sentence "der Gerry-Mann"... so it's just a man named Gerry! (this is sarcasm, i also have no idea what gerrymander means)

[@Izzythemaker127]

@@lukasjetu9776 I think it was named after some Gerry guy who made a district shaped like a salamander and got the practice of rigging elections by making weird districts to group voters advantageously named gerrymandering

[@aurusallos]

@@Monkeymario.​ @lukasjetu9776 "gerrymander" is a noun-version of "gerrymandering", which is an American political practice to manipulate raw direct votes into representative districts to minimize/maximize representative voting results (typically to allow the conservative party/Republicans the most representative power on the national level). It produces very complicated shapes.

[@dr.szilassilajos]

It's amazing how much this problem has evolved over the last nearly fifty years. I'm proud to have been the one who started it. Congratulations. Lajos Szilassi

[@EDoyl]

Without a proof this is not at all solved, but you discovered a cool shape which is imo cooler than solving a little-known problem. Like you can show that 3D printed razorcross to people like this is the shape I discovered

[@leif1075]

Dodnt he present a visual.proof and so bow is it.not.solved?

[@aaaa-d7p8m]

@@leif1075 since the shape he presented isn't a valid shape (it intersects itself). The positive result has not been proven yet. If it were a valid shape, then you'd be right, it would be solved. Similarly, the negative result has not been proven yet since he hasn't proven that this shape is truly the global minimum.

[@BetaDude40]

@@leif1075 His example shape has self-intersections so it's not valid as an example of the proof being true. It is still impressive that he got that close with a heuristic approach, but unless he can find a non-intersecting version this neither confirms nor denies the existence of the true polyhedra

[@stanley8006]

@@BetaDude40I’m more interested in the possibility that this is could be true mathematical “limit”. No matter how strong a supercomputer filled warehouse’s mathematical processing power is, the solution finding algorithm would always and without failure find itself discovering and rediscovering the razercross or not discovering any other shape that fits the bill better than the razercross. The chances are slim but it’s fun to think about, and I hope this endeavor to find a crossless intersectionless face neighboring 6 hole donut is taken up by a mathematical institution with the power to tackle it

[@chriss1331]

​@@sammxn-w2v it has self-intersections, which makes it not a valid solution. Did you watch the video?

[@itisALWAYSR.A.]

Omg i got a handful of 3D-printed Szilassi polyhedra a few years ago at an event... and when I got home I forgot what they were for so i just had a bunch of mutated caltrops in my living room and i had no memory of their feature. Thank you for allowing me to successfully pin it down without using a search engine - the universe provides!

[@firefly618]

Here's an idea: have you tried turning the problem into a differentiable one? Instead of assigning a value of 1 or 0 to each crossing or intersection, you could compute an "amount of intersection" where each pair of faces contributes a value of 0 if they are not intersecting; > 0 if they are, with an amount that tells how much they are intersecting, such as the length of the intersection segment. Something similar might be done with crossings. This way you could use automatic differentiation to compute the gradients of the entire construction, and then use one of the gradient-based optimization algorithms.

[@nikkiofthevalley]

Huh. That should make it possible to run a swarm gradient descent and run the whole thing on a cluster.

[@MrCheeze]

Well, I'm definitely calling the theory that this shape is optimal "CodeParade's Conjecture".

[@jffrysith4365]

Good name, because that's what it is.

[@poke7661]

THE HENDECAGONAL DODECAHEDRON????

[@thietnguyen5603]

A 12 SIDED POLYHEDRA WITH ALL HENDECAGONS?!?!?!

[@poke7661]

so sad that they couldn't generate a fully intersectionless solution but hey still cool

[@fgvcosmic6752]

THEY CALL IT THE WHAT???

[@fgvcosmic6752]

A POLYHEDRON OF SORTS?

[@jwc1284]

WOAH!!!!!!!

[@DrTrefor]

This was such a great video, had the feel of a @StuffMadeHere video but entirely for a math problem. Seeing first hand all the attempts and tweaks on it is cool and I wish we got to see more of the process behind coming up with ideas, so often in math we get the final polished paper and voila there it all is but not the process

[@whoeveriam0iam14222]

summoning geometry

[@TreesPlease42]

6:45 what an iconic moment right into the womp womp horn from Price is Right

[@RealElevenTimes]

dash

[@Kknewkles]

"You friendly neighbour polyhedra, Szilassi"

[@juergenbokowski]

The proofs (by Bokowski and Guedes de Oliveira in 2000 and later by Lars Schewe in his Ph.D.) that have clarified that all 59 neighborly dual examples (closed 2-manifolds with 12 vertices and 44 triangles) cannot be embedded without self-intersections have used a combinatorial tool that leads to a finite number of cases (although this number is very large) before the search for a corresponding matrix begins. In all cases the set of the allowable cases for searching for a matrix was finally the empty set. Perhaps this is in the dual case again the appropriate way to solve the problem. This combinatorial tool has many sources. You use labels for all vertices of your point configuration in 3-space you are looking for, every subset of 4 points forms in your solution a tetrahedron (perhaps generated) with orientations 0, -1, or +1. Forbidden intersections of an edge with a triangle of your face tell you a forbidden set of five such orientations. The theory of oriented matroids might tell you more how to proceed.

[@Bolpat]

14:50 Without a formal proof, it's not hard to say. Without a formal proof, the answer is: Absolutely not.

[@YoReid]

He's using the word 'solved' to refer to whether or not the optimal shape has been found, regardless of a proof

[@RydPodoJosh]

Dork lol

[@aaaa-d7p8m]

@@YoReid From a math perspective though, a problem being solved refers to there being a definitive yes or no with proof.

[@TheWolfboy180]

okay nerd

[@GOATaro_]

The absence of a proof doesn’t mean there isn’t one.

[@TRex-fu7bt]

5:52 nice Summoning Salt style line graph too

[@yoobinator]

We love the summoning salt references

[@Dr-Tehnix]

Did not expect to see a summoningsalt style math discovery any% run today.

[@Koroistro]

I wonder if this algorithm could be rewritten in such a way that it can run on a GPU, an exhaustive search would be in realm of possibility.

[@davutsauze8319]

Exhaustive? There's an infinite set of possibilities to look through, right?

[@Juniper-111]

At 3:05, you claim that a solution would need 12 faces and 6 holes. According to the wikipedia article on the Szilassi polyhedra, the only stipulation is that # holes = (# faces - 4)(# faces - 3)/12 which has infinitely many solutions. Do you have another source for 12 faces, 6 holes being the only valid possibility? If not, have you tried 15 faces 11 holes or other solutions? edit: I just realized that you don't have a nice source listing all embeddings of K15 on manifolds of genus 11 :( But, I just wanted to point out that the possibility for solutions with even higher genus was missed in your video.

[@CodeParade]

Yes exactly. If I can get a list of the K15 manifolds I could try finding more solutions, but I'm not sure how to generate them. Also I think there's exponentially more manifolds to check as vertices increase.

[@muharremsuz]

​@@CodeParadeso why you clickbait on the title if you already know you dont solve anything?

[@hazelharry2033]

​@@muharremsuz Cuz videos need views to be spread around

[@muharremsuz]

@@hazelharry2033 he is a researcher right. He knows what ethical or not so he must be change title to not clickbait people.

[@JamEngulfer]

@@muharremsuz The title is a question that can be answered with “no”. It’s on you for assuming that it was “yes”.

[@henryzhang3961]

I was so excited to see it lol. I'm still holding out hope that another true neighborly polyhedron exists

[@lightninghuff]

I literally obsess over these same shapes sharing properties of the tetrahedron. Thank you for the insightful video! 🙌

[@robbiekavanagh2802]

Cool shape! Congratulations! Great that you're opensourcing your work!

[@whynotanyting]

12:17 Looks like a pterodactyl with its wings on a down stroke.

[@Ganerrr]

did you re-detect the known solutions?

[@CodeParade]

Do you mean the Szilassi Polyhedron? Yes, it finds that solution immediately when I use the Heawood graph as input. If you mean the same best solutions with other random seeds, yes at least 10 to 100 times each.

[@Smol_Schan]

Okay, so I immediately have an idea, which is to just take all the outside faces of a platonic solid and extend them out into planes until they intersect the other edges. Then, you can find where those planes intersect all the other planes to create the edges. That visualization could help you look at the problem from a different angle.

[@Smol_Schan]

I'm just going to add, this should work for any shape without parallel faces.

[@Smol_Schan]

I actually thought that this was the solution you were going to go for as well, funny enough.

[@gehirndoper]

That's a pretty cool approach and you got very nice results. But the answer is no, you did not solve the problem.

[@TheGrimSmile]

That's really the toughest thing about proofs. We've had years between discovered prime numbers, we can't call it done just because we haven't found a new one in a while (indeed, we'd be provably wrong!) It might make a good starting point for attempting to prove it, though.

[@gehirndoper]

@@TheGrimSmile Wdym we've had years between discovered prime numbers? Your phone generates dozens of new prime numbers every day for encryption etc. each day

[@bosstowndynamics5488]

​​@@gehirndoperYears between each instance of discovering the *largest known* prime number, not an arbitrary already known prime number. The prime numbers used for RSA encryption are usually no larger than 2^2048, although depending on implementation 2^4096 is reasonably common as well (and represents the absolute ceiling in available implementations). To put that in perspective, the largest currently known prime number is 2^136,279,841 - 1, on that scale 2^4096 approximates zero.

[@ethanbarnes9333]

13:36 but acerola

[@Purely_Andy]

good reference

[@McLyTheChannel]

Nice

[@Goofyahh_shark]

Nice

[@soul-t100]

12:20 CALL IT THE PARTY DUCK🦆

[@JToH_Lover]

11:22 The Triquadrexipentanonahedron

[@Sebastian-kx4nu]

I call it The “Erisohedron”, which is a reference to Eris the Greek Goddess of chaos and strife. And this shape seems to reflect the sense of ‘perfect’ chaos.

[@vitorportosilverio5820]

I call amerisinviholedron Erisedron Mikerikitodron Monthedron Ending MMXXIV polyredron Misterydron

[@SevenAdamson]

I call it the docecaerisodexdodecangle

[@ЯндексПеревод-з6у]

11:19 Parker polyhedron

[@iamwhatitoture]

No, he switched from Python to C++

[@iamwhatitoture]

No, he switched from Python to C++

[@iamwhatitoture]

No, he switched from Python to C++

[@pandamaster8306]

12:16, I would suggest "The gerrymandered district"

[@kiwibirdnuevazelanda]

Map men, map men, map map map men men men.

[@salmiakki5638]

Every time this channel posts, i'm in awe at the level of handiness this man has with mathematics and CS. I envy it and aspire to it, but I think it's too late for me to be reachable. not too long ago I tried to think about some optimization problem of some practical problem i wanted to write code for. i still have it in the back of my mind and i'll probably go back at it sooner rather than later, but i got so frustraded i didn' had the mathematical tools to be able to reason about it

[@tetradigit]

Man, what a journey! Thanks for documenting your process like this. Really inspiring! And thanks for linking your github :-)

[@KnakuanaRka]

A few things: In addition to face-neighborly polygons, there’s also corner-neighborly ones where all corners are connected, duals of the face ones. The tetrahedron is its own dual, but the dual of the Szilassi is something called the Czaszar polyhedron (IIRC, may have misspelled it), which I think could be a bit more digestible than the Szilassi. Would a corner-neighborly for this be easier to construct? The minimal-crossings one shown at 14:28 looks almost exactly the same as the Szilassi with a bunch of extra stuff in the middle; makes sense. Third, there’s some better names for the faces of your Razorcross; I’d call them the Sail (turn it CCW a quarter, like a sailboat), the Spade and either the Pipe (the kind you smoke with) or the Note 🎶.

[@lightninghuff]

Exactly. Part 2 should be looking at the opposite problem with the Csaszar polyhedron properties. In fact, what are the properties of the dual to the razorcross? 🤔

[@louiebr7620]

0:00 whenever i hear that music i know something crazy is about to happen lol, i just really enjoyed all the summoning salt references, like the crosses graphic lmao

[@darraghmooose]

The Pointy-Headed Duck shape really reminds me of the shape of the state of new york, just a bit out of proportion. Also amazing video king, thoroughly enjoyed!!!

[@PunmasterSTP]

This right here is the absolute best of what the internet has to offer. Godspeed man!

[@yew7607]

This is awesome, super frustrating that you couldn't find a perfect solution but this was super cool approach

[@jodinha4225]

I think someone ought to reprogram the solver to run on the GPU. I'm not sure how GPU fairs relative to CPU with this particular kind of math, but broadly GPU is better at these sorts of brute forcing tasks...

[@BetaDude40]

@@jodinha4225 It wouldn't make that much of a difference in terms of solvability. If there truly is no such valid shape then a proof by exhaustion would basically require testing every possible polyhedra which matches the form of each manifold (i.e. way more than is computationally feasible). If there is such a shape but we're trapped at a local optima, then it would be difficult to find a way to optimize further to reach the globally optimal polyhedra (and this is assuming we know one exists).

[@macratak]

his approach is very bad

[@BetaDude40]

@@macratak Fine I'll take the bait, what's so bad about his approach?

[@BeaDSM]

The seven-sided one was far less symmetric; would removing the symmetry constraints to make perturbations on your 4-crossing polyhedron perhaps give you an ever smaller crossing option?

[@ProgrammingWithJulius]

This is one of the coolest videos I’ve seen on KZbin lately

[@JosiahPlett]

The summoning salt music, font, graphs, and storyline goes so hard

[@MajikkanCat]

You definitely solved "what's the coolest polyhedron you can make out of 11-gons." :-D

[@AJMansfield1]

For a continuous cost function, what about 'sum of intersecting edge lengths'? The other thought is that the 'collinear edges' situation feels like it could be important, with a face that neighbors two or more other faces along one otherwise-straight edge.

[@AMan-xz7tx]

"huh, haven't heard from code parade in a while, I wonder what he's up to?"

[@TheRealFOSFOR]

They all have striking similarities to the simple tetrahedron tho. Its almost like you just need a tetrahedron and start shaving it down and cutting holes in it.

[@kevincsellak296]

I love that name, the Razorcross

[@asailijhijr]

The shape you've called "the pointy headed duck", I'd prefer to call it 'the trowel and arm'. I see a triangular hand-tool being held be a bent (human) arm (severed at the shoulder).

[@whoeveriam0iam14222]

I expect Matt Parker to make a video about this now

[@AntiVectorTV]

It's so tantalizingly close to a general algorithm for generating these things, given the similarities between these shapes. Note that the farthest points from the center in both the Szilassi polyhedron and this form a tetrahedron.

[@EXL_BOY44]

0:23 that ilustration is the 92 Jhonson solids

[@TurbopropPuppy]

i wwould'vve called the Pointy-Headed Duck the "Cartoon Bag of Money" personally

[@craftminerCZ]

What's funny is all the near-solutions you continuously kept finding seem they're converging to look like Szilassi polyhedron, which itself looks like a tetrahedron with those 2 perpendicular edges across each other (assuming the center of mass is the point at which all of the symmetry rules you mentioned intersect, I ain't doing math or any actual thinking xd). I wonder how math problems clash with the definition of a floating point number and how those problems are resolved.

[@psymar]

So my immediate thought is: could you try some random peturbations of the symmetric one, but with the symmetry constraints turned off? Given how close it seems to be to being intersection free, maybe some small asymmetric changes would do it?

[@michaelspringer6747]

someone make this into a rubik's cube

[@pinkshortcomedy]

12:22 the gerrymandered county!

[@Sebastian-kx4nu]

I’d call it “The Pinkie” cause’ it looks like a pinkie finger.

[@JosephMartinez-yc6rb]

As soon as I heard the music I knew this was gonna be peak

[@darkonyx6995]

Ngl Razorcross is actually a really dope name for a shape!

[@TheNeraum]

I thought you just found the HOME song because it's good royalty free music, but then I saw the title card and later the graph and this is fully a summoning salt homage with a vastly different topic, incredible haha

[@Salamander876]

For a neighborly polychoron, you’ll need to regard overlapping of two vertices, crossings of two edges, intersections of two faces, AND the intertwining of two CELLS.

[@loganseawright1173]

I love that just by listening to what background music is used during the video we can now determine whether or not someone was influenced by summoning salt

[@matthewparker9276]

The fact that you got either 4 intersections or 4 crossings aounds kinda significant. I wonder if you can get lower combined crossings and intersections, like 1 crossing and 1 intersection.

[@BattlesDiplomacy]

Loving the Summoning Salt aesthetic throughout!

[@nexonnera.k.a.8796]

Oh man, you really should have used a proper parallelized runtime that's actually good for math and science like taichi or numba or just run several solvers at the same time!

[@dylaann]

I haven't finished the video but my guess is that the answer is to symmetrically mirror the 4 sided pyramid, rotate it such that only 1 edge lines up, remove the negative space that both pyramids occupy, and then shave off the extra bits so its flat on the side that's "inside" the hole, then mirror the remaining shape and repeat

[@CaptainAOrange]

If you rotate the pointy headed duck 90 degrees, it looks like a rabbit, with the pointy bit being the ear and the less pointy part being the head with a nose. It also is kinda a reference to Alice in Wonderland in the sense that you followed a white rabbit, and that Lewis Caroll was a mathematician.

[@emilev2134]

This deserves a @numberphile video!❤

[@omegastar2508]

The Vsauce short to this video pipeline is insane

[@giacomosoncini3237]

For the name of the faces i suggest: -the shark -the duck (the upper triangle is the head) -the sailboat (the head and the hat of the “duck” is the sail and the body of the duck is the hull) Just a suggestion but I think is a good one

[@cupcakesandrose]

Has anyone ever seen CodeParade and SummoningSalt in the same room together?

[@ssamuueel]

"light blue, dark blue" *those are literally the same colour*

[@pierreabbat6157]

Russians disagree: голубой, синий.

[@bosstowndynamics5488]

​@@pierreabbat6157Just to confuse things further, KZbin translates both of those words to "blue" (although I am aware that you're referencing the fact that what's called a separate colour is defined culturally through language rather than objectively, just noting that YT messed it up somewhat)

[@05degrees]

@@pierreabbat6157 I guess @ssamuueel meant that visually colors of those faces look indistinguishable. Probably a lighting issue, maybe in the room those really look different but on video it’s as if they’re the same.

[@VcSaJen]

@@pierreabbat6157 Not really. Both of those colors are "синий".

[@LightslicerGP]

11:04 dude this shot is incredible

[@_arie__]

You know it's gonna be great when the vid has summoning salt type of intro

[@pronayghosh]

Must be a coincidence right! Micheal just uploaded a video related to this!

[@LimeCider]

man i love CP... CP has content i could watch anyday!

[@arcade_frog]

Please can you attach the 3D file as a link?

[@enderwiggins8248]

I loved the Summoning_Salt graph and music cue, great reference 😂

[@VeryMonkelol]

15:03 DETERMINATION

[@alhello_game_of_everything]

FINALE

[@Vasof67]

But it refused

[@andrewgeier567]

Why do the polygons have to not have 180 degree vertecies? what if a solution has some faces with 11 sides and some with less?

[@TheOneMaddin]

While you did not solve the problem you made significant progress and should absolutely go for publishing it in a scientific journal!! You could go for "Experimental Mathematics" or "Discrete and Computational Geometry", or aim higher.

[@amits4744]

4:02 even f=15,16,19,24 and many more yield whole values of h Maybe going with any of them can give a larger polyhedron with more faces and holes but having the property that all faces share atleast 1 edge with each other and without any intersections. Maybe f=15, f=16, f=19 or f=24 can give such a polyhedron

[@chrispysaid]

The answer to the title is always NO when it ends with a question mark

[@jell0goeswiggle]

@16:04 Ooooh that's where i recognized your channel from! Not at all surprising you got nerd sniped by a math problem like this.

[@elementgermanium]

The small size of the intersections bugs me. I just get the vibe that there must be SOME way to get rid of them, some way to just barely squeeze around them… maybe this is a local minimum, but an attractor for the optimization method somehow?

[@petevenuti7355]

My first thought too, and so close .

[@niuage]

There are so many cool things about this video. Very impressed by your skills as well. I also love how the 3d printed shapes could easily be art pieces.

[@Owen_loves_Butters]

Heuristic arguments aren't as strong as they seem, so I'd caution against saying it's "very unlikely". Still, I do strongly encourage everyone to take a stab at problems like this. Not because it's particularly likely that you'll find the solution, but because what you learn along the way is also valuable. Easiest example is the Pólya conjecture, with the first known counterexample being greater than 10^361.

[@alebenny78]

Really extremely brilliant! And also a perfect work completed along all the aspect, including the pratical production of a sample!

[@onedeadsaint]

13:42 bold prediction. guess time will tell.

[@diamantnt]

What

[@thepinkbunnyempire1027]

The Szilassi Polyhedron is my favorite shape, which makes me excited for this video!

[@ralakus8784]

12:16 Could name it "The assassin" since it looks like a hooded person holding a comically large kitchen knife