The Mysterious Hyperdice Sequence

[@xbolt90]

Always was jealous how the fourth dimension gets one more platonic solid than we do. 4D D&D must be pretty fun!

[@sapphiresuicune6787]

😂😂😂

[@stevenjacobs2750]

More dice doesn't equal more fun haha. Single dice systems ftw

[@TheBasikShow]

Would they call it D&D&D?

[@publiconions6313]

Lol

[@MeshremMath]

The rhombic dodecahedron is the 3D equivalent to the last 4D polytope.

[@stickfiftyfive]

The Fourth Dice-mention. So. Very. Excited.

[@Lugmillord]

The only channel where the clean up is the most time-consuming part of video production.

[@danieloconnor4638]

Super vid! Jan Misali has a video called "there are 48 regular polyhedra" that explores more concave polyhedra and other weird shenanigans like the "spiky" polyhedra that Domotro talked about.

[@SunroseStudios]

was gonna comment this! very good video

[@Hamboarding]

Me too, I should have looked for the comments first!

[@clutchbridge]

So was I lol. There was also a small part of me that just expected to see him randomly comment on the video himself

[@mesplin3]

Right... I was a little surprised that he didn't mention why the hexagon tilling of the plane was not considered.

[@vii-ka]

Here is the link: kzbin.info/www/bejne/lZnNg6mQjtB0naM I just realised people will think I am a bot, but no this is the video mentioned.

[@bonecanoe86]

I bet if they showed your videos in school a lot more kids would be interested in math!

[@iamdigory]

Do-mo-tro the math guy!

[@gabrielbarros493]

Some would be disencouraged

[@ghastlyGrenadine]

the only guy to simultaneously use both the singular "verticie" and the plural "vertexes"

[@gary.h.turner]

Perhaps he also thinks the plural of "spouse" is "spice"?

[@RyanSnead]

Squirrels like the one appearing in the video at 12:48 are natural experts a gliding through the air which I noticed is the Platonic element being discussed at 12:48. And 12 which is the number of minutes elapsed in the video can be multiplied by 4 to make 48 which is the number of seconds in the video which makes that particular neighborhood squirrel a very special guest in this video.

[@Wyrmfell]

I've known about the platonic solids but never knew *why* they were the only ones, really good job explaining!

[@sketchditty1054]

I really appreciate you bringing a fresh and interesting way of teaching math. Not just your topics but you as an entertainer is what makes this channel so special. Keep up the awesome work!

[@coltenh581]

I’ve maybe never understood the “spherical x in a vacuum” joke more than I did when you had to put up the info card with all the caveats and precise language 5:30

[@ww4830]

I love how loving and silly your videos are. Makes all of this complicated geometry seem so simple!

[@darkstar342]

Dude, you're making awesome stuff, glad I found your channel.

[@connorhart2793]

Just love this guy, the perfect mix of entertainment, enthusiasm and education.

[@lexinwonderland5741]

This guy is fucking crazy. I love him. He's so excited to share and obviously the chaos aesthetic does him well. I feel so understood by him, this is about how it goes when I show friends or students my corner of academia. Subscribed!

[@thatssokwekwe]

This channel should be required viewing for any mathlete

[@Metaller1982]

dude you're like a weird mix of explosions and fire and numberphile i absolutely love it!!

[@DecayedPony]

This channel is by far the craziest most entertaining mathematics related thing I've ever seen. Amazing

[@1234567zeek]

A "normal" person would require about half a year to produce this video. I catch myself laughing when I'm mentally saturated. Thank you for the excellent videos.

[@jesnoggle13]

Funny and informative and really dorky. I’m hooked!

[@tjeepert9782]

I literally can't express how much I love this video and your entire channel. KZbin needs more of your style.

[@jmm1233]

Nice cameo for the squirrel

[@evancherpeski1876]

This is my favorite new channel; every video is very good education and entertainment!

[@chinmayjoharle9065]

This is one of the most interesting channels I've seen. Keep up the quality videos man 👍

[@sirludicrous7823]

Awesome content, awesome video But is nobody going to talk about the scream at 2:20? xD

[@vanevarnel7131]

Thanks great video. I love the lab coat and the desk. Good job filming the video out in the fresh air.

[@azimuth4850]

Loving this series. Learn something I didn't know each time.

[@qmoyer]

Hi Domotro! I've always been fond of the dodecahedron and the truncated icosahedron. Stellar video today!

[@jacobbates7766]

A beautiful sequence and a brilliant explanation! This is some of the most awesome educational content I've seen and it's really inspiring, can't wait for the fourth dimension!

[@garlicbread5214]

Very cool to see more videos on the regular polyhedra. This also explained duals much better than Jan Misali's video that went into like all 40 or whatever many shapes there actually are without the restrictions you mentioned at the beginning.

[@ThomasHaberkorn]

Your style is quite unique, love it

[@peppermann]

You have a truly gifted way of explaining both simple and complex maths topic Dimitri, I’ve taught about the Platonic solids for years and you’ve out-taught me without even trying.

[@james10492]

This content is so good... you sir - kudos.

[@publiconions6313]

So glad YT put this dude in my feed - wonderful!.. good thing about math channels is there no shortage of fascinating content.

[@ПлатонАнтонов-о9я]

i love the quality of your lessons and the amount of jokes. Your channel is amazing! hope you get some more subscribers soon 💜

[@rhodesmusicofficial]

Your style of presentation is super refreshing! Really great stuff man

[@natalie5947]

I've seen about 6 combo class videos by this point and I'm still not acclimated to the chaotic energy demotro brings.

[@infinitesimalperinfinitum]

I don't know how you're doing it, but please continue spying on my watch history and releasing videos that explain the things I'm unsure of. It's unnervingly helpful.

[@frimi8593]

God these videos look so fun to shoot. I can’t wait for this channel to blow up

[@vincentv.3992]

Thank you so much for your awesome videos! I would love to see the net of a 4D-Hyperoctahedron!:-) From the 4D-Hypercube, one can easily find many representations, but not from the other ones.

[@marveloussoftware1417]

Very cool!!

[@kikivoorburg]

I vote that we replace “non-convex” with “nonvex”. Now that I think about it I’m not actually sure if non-convex implies they’re concave or if there are shapes that count as neither

[@aliasjon8320]

I thought pop culture desensitized me to mad scientists, but this guy is a mad mathematician

[@chri-k]

A mad mathematician might be worse than a mad scientist

[@wesleydeng71]

12:47 A squirrel visits your backyard!

[@iranzijlion7674]

Thanks man, your videos are helpful. Keep delivering 👏

[@Kreypossukr]

I LOVE your channel and your videos, keep up the good work !

[@zeshan144]

I do love your channel, I have recently took an interest into maths and enjoy geometry and number theory which I see you do alot of. Thanks for the help 😊

[@BaldRocket]

Your stuff is incredible! I’m glad I came across your channel

[@sillypilly1234]

Great video! lots of interesting stuff and entertaining

[@thejaywalker8922]

I love your videos man!

[@RandomAmbles]

Quick shout-out to the 720⁰ "angular defect" of all convex polyhedra and the free 3D-model-to-2D-net program Pepakura! Shapes - shapes everywhere!

[@HomieSeal]

Glad to see another video from you :D I’ve only seen a tiny bit so far, higher dimension shapes have always been very cool so this will be interesting

[@charlygutierrez1338]

Gosh, as i said before, i'll watch every video until i get it, bc the way you're skills teaching are amazing!! Greetings from México lol,

[@themetal]

I can see why Plato believed the gods my have used 12 faced figures to create the universe; coincidentally, or not, 12 is a very important concept that regularly appears throughout almost everything.

[@sthubbar]

Thank you.

[@paulfoss5385]

The d10 is the dual to the pentagonal antiprism (two opposite facing pentagons on parallel planes joined by ten alternating triangles) The pentagonal antiprism has all identical vertices but it has two pentagonal faces and 10 triangular, so its dual has all identical faces but the vertices aren't all identical, which is why the faces are kites. Interestingly, the cube can also be viewed as the dual to the triangular antiprism (the octahedron). Notice how the d10 has kind of a zig zag equator. Hold up cube/d6 by antipodal vertices, and you can see the cube as also having a zig zag equator.

[@Gunbudder]

my favorite concept about higher dimension geometry is that the more dimensions you have in a vector, the less meaning its distance from another vector has. or another way of putting it, if you calculate the distance between two n-dimensional points, that distance has less meaning as n grows to infinity. What i mean by "meaning" is that the distance has less information and becomes less useful for analytics. i cam across this when studying machine learning with massive vectors doing something like nearest neighbor. the classic example is a dataset that is a huge list of 22D vectors, each one corresponding to a yes or no. you train your nearest neighbor system on that, then feed it a new 22D vector and see if is closer to the yes or no vectors. Well, my thinking was if 22 dimensions is good (and you literally use an expansion of the distance formula for 2D space) then why not 220 or 22,000,000 dimensions? well i found that the research had already been done, and they found that for sufficiently large dimensions, the accuracy of determining if an unknown vector was "yes" or "no" dropped from 97% to something like 50%, which was worse than the crystal ball method (just guessing). its not too much of an issue though because most practical applications of this method of machine learning use physical parameters of some type. even "big data" has a practical limit on a vector, which is often a person. there are only so many things amazon can measure about a human to determine if they want to buy something or not before they show it to that person. also neural nets just kind of blasted past that method of machine learning at mach 10 in the past few years, so it seems like no one really cares about it anymore anyway lol

[@potatoheadpokemario1931]

there is a hyper Dimond in the third dimension, it's just not a perfect shape, it's called the rhombic dodecahedron

[@brandonstokes5927]

great video as usual

[@FirstLast-oe2jm]

incredibly fun video as always

[@steelegagnon5273]

can’t wait for 4d 😝😝

[@epicdaniel508]

This is amazing

[@Dracopol]

12:47 A squirrel scurried by!

[@alamagordoingordo3047]

I'm so fascinated by geometry in higher dimensions.

[@flockofwingeddoors]

Just discovered you the other day, love what you're doing with your videos! The chaotic energy really compliments the math. Very interesting at 1.5x speed haha Also, isn't there an argument for infinite regular polytopes in 1D since you can make your like of any length you want? Alternatively, it should be zero since it doesn't enclose an area?

[@ComboClass]

Thanks! About your questions: different sizes of line segment wouldn’t count as different types of polytope, similar to how different sizes of cube all count as the same type. The specific length doesn’t matter, what matters is how the edges/sides/vertices go together, and if you considered different sizes as different types then any of these dimensions would have an infinite amount). And the generalized “hypervolume” of a shape’s interior in 1d is length (then in 2D it’s area, in 3D it’s volume, etc)

[@OrangeDrink]

I would guess on 2d the shapes that tesselate the plan would only be counted, but regardless watching you smash math to pieces is fun thanks

[@OrangeDrink]

First hyperdice. Imagine the shape of infinite -1 size, a circle difference from a triangle would a walk across verticis even be visible/measurable. My assumption is that all variables include if your whole perception was greater than one unit the answer is no, but if your perception was an infitesimal or slightly greater then it would be not perceived

[@MabInstruments]

A 3D equivalent of the 4D 24 cell is the rhombic dodecahedron, though it isn't regular, of course.

[@cec4]

this is top quality stuff

[@PhilHibbs]

The ten sided shape is a dodecahedron with two opposing faces extended out to a point.

[@insanitycubed8832]

There are actually a lot more fair dice than that. A fair die is pretty much a polyhedron composed entirely of congruent polygons and have some platonic solid symmetry. That definition may fall short, but for instance catalan solids can make fair dice. Edit: I wonder how many of those are in each dimension. Also forgot my manners. Cool video, and cool squirrel too

[@calebclark9114]

Nice video! Also did you compose the music in the intro?

[@ComboClass]

Yeah I made all the music in this episode (and many of the episodes)

[@calebclark9114]

@@ComboClass 😎

[@TheMayzeChannel]

combo class ost mixtape when domotro?

[@ComboClass]

@@TheMayzeChannel I'll definitely release more musical projects when the time is right :)

[@TheMayzeChannel]

@@ComboClass sweet

[@denischen8196]

Is it proven that there are only 3 regular convex polytopes in higher dimensions? Is there any hidden 5D or 6D polytope that has yet to be discovered?

[@boghag]

It's proven. They don't fit around the vertices anymore, but you can always make a Simplex (Tetrahedron equivalent), a Hypercube and the Dual of a Hypercube

[@noahnaugler7611]

That's the thing though, dice only have to be Isohedral, not regular. There are infinitely many Isohedral figures in 3 dimensions, but only 5 regular figures. I'm really curious about the limits of the convex isotopic (cell-transitive*) figures in 4 dimensions. What kinds of fair 4d dice are possible? * I came up with this term myself, based on the etymologies of "isohedral" and "isotoxal", so it may be incorrect, but I couldn't find an alternative in my admittedly brief research

[@Brunoenribeiro]

12:47 "Aaaaaaair..." **squirrel**

[@november666]

Domotro is such a cool name. It sounds like someone from a comic book

[@katiebarber407]

I recently watched a great video dealing with non-con vex polytopes. I forget exactly what it's called but something like " there are 47 shapes "

[@DIPHENHYDRAMINEMAN]

I love this guy :)

[@tilnation14]

My problem with calling them hyperdice is that there are a bunch of other shapes, like the catalan solids, that also work. Wolfram has a nice list(I guess this list is exhaustive) of 30 isohedron that would all work as dice (although a few, including the tetrahedron, don't have a 'top' face, making using them as dice more difficult).

[@jesnoggle13]

The tetrahedron is also special because it hurts the most when you step on it barefoot.

[@asdf30111]

Way I learned to "imagine" 4D for example tesseract, pick the "middle slice" of your shape, in this case we get a cube. Color it purple. Superimpose a red and blue cube on the same exact spot. Then between the three cubes, add more cubes of increasing and lowering amount of red and blue color until you connect the structure together. Though sadly very hard to keep a stable picture or even to rotate it in your mind.

[@veggiet2009]

More 4D videos!

[@MrKyltpzyxm]

Salt is a mineral. Salt is a cube. Earth is minerals. Earth is cubes. Vindication for Plato! 😂

[@simonwillover4175]

2:35 - I like how we can hear the Neighbor's kids in the background.

[@ComboClass]

I’ve talked to that neighbor, he’s nice. We’ve discussed the noise and are both cool with each other :)

[@erdmannelchen8829]

12:01 Didn't know that Play Dough is that old.

[@DragonslayerProd]

"Cubes were believed to represent earth" Mojang wants to know your location

[@Skeleton-bs7zy]

Distilled crazy math man

[@Dracopol]

The reason for the number-sequence 1, infinity, 5, 6, 3, 3, 3...was already covered in this video. kzbin.info/www/bejne/aKSXhaSMdseZsJY

[@realNom2mooncow]

2:20 & 2:36 screaming in the background lol

[@ComboClass]

Neighbor's kids lol

[@azimuth4850]

Yes it fit quite while with the video

[@christosmani]

Squirrel was a paid actor!😂😂

[@ThisCanBePronounced]

"don't copy any actions from this video" I shouldn't do math? D:

[@ComboClass]

You can copy all the knowledge from the video. Just not the parts with fire and falling clocks and breaking desks :)

[@HomieSeal]

@@ComboClass instructions unclear, calculated how many 3d hyperdice shapes are needed to break my desk and make all of those dice fall over

[@ThisCanBePronounced]

I don't know, desk-breaking looks highly educational. 😜

[@malicholson5767]

so care to explain the 48 regular polyhedra described by yan misali i found that video interesting

[@ezhanyan]

12:48 omg, a squirrel

[@maht0x]

even god plays dice, Plato said

[@good.citizen]

🎲 thank you good luck.

[@kirbymia6209]

You make maths interesting.😆

[@amesstarline5482]

The cube representing earth is fun, considering Minecraft.

[@melody3741]

I've heard people say vertexes before but I've never heard people say vertice

[@melody3741]

You should exclusively say "vertice" and "vertexes" just to piss people off

[@dranorter]

What about Catalan dice though??

[@kittyn5222]

Rip desk: always dying-

[@Fred-tz7hs]

HYPER HYPER