There are SIX Platonic Solids
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- Опубликовано: 1 июл 2024
- Meet the Hyper-Diamond! It's the sixth Platonic Solid and it only works in the fourth dimension.
Your best google bet to find more about the hyper-diamond is "24-cell".
mathworld.wolfram.com/24-Cell....
Watch my Royal Institution lecture about 4D shapes:
• Four Dimensional Maths...
My book: makeanddo4d.com/
Maths Gear: mathsgear.co.uk/
4D animations made with Stella4D: www.software3d.com/Stella.php
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Music by Howard Carter
Design by Simon Wright 
Развлечения
Guys, the video by jan Misali is about *regular polyhedra,* not platonic solids. There are 5 platonic solids in 3D.
*thank you!* how can so many people be maths enthusiasts and not know this??
Matt repeatedly conflates the platonic solids in 3d with the regular polyhedra. "Despite the infinitely many 2d shapes, there's no other way to join them together to make a regular 3d shape. We only get those 5 platonic solids"
@@pipolwes000 to be fair, there are only 9 regular polyhedra in 3d. Nothing Jan mentioned after the Kepler-poinsot solids was actually a polyhedron.
@@LeoStaley *finite polyhedron anyway
There are only 5 regular convex polyhedra (as the other 43 are not convex).
@@LeoStaley If a shape in 3d space is face-, vertex-, and edge-transitive, then it's a regular polyhedron. Nothing about this definition precludes shapes with infinitely many vertices. The regular planar tilings meets these conditions (I think trivially), and so unless you use a more restrictive definition, the tilings are regular polyhedra.
I wish I hadn't subscribed to this channel.
so I could hyper-subscribe.
It's ok, I'll upgrade your subscription for you.
+standupmaths where can I hyper-hyper-subscribe
+CharTheDude 6:17 Top Left Corner!!!!!!!!!!! CLICK IT BEFORE THE HYPER DIAMOND REVERTS TO 3D AND TEARS SPACE TIME KILLING US ALL!
Bam, just hyper-subscribed.
@@standupmaths What about the video of they guy sayi ng t here re are ac tu ally 48 regular platonic solids? Do yiu need to update this?
I hope your animator got a raise...
He did. Into the fourth dimension.
Stella4D look in description
I hope the computer got a graphics card upgrade, cause jesus christ that would take a lot of rendering power
You cannot donate to Wikipedia
@@Ewumm not really. Those are just vertices connected with lines, and there are only hundreds of them. Modern games have a lot more elements in one scene, yet no complicated lighting, fancy shaders and all the 'difficult graphic' stuff. The animation can be run on any pc, even laptop. I've got more questions about building the shapes. (that involves CPU btw. And a fair amount of intellectual work to write the program))
I'm just here to hang out with all the jan Misali fans insisting there's 48 platonic solids
even though there's a difference between platonic solids and regular polyhedra, and his video made that pretty clear, I thought
He didn't make it clear, but he also didn't make it clear that he was using extremely non-standard definitions of both polyhedra and polygon. The universal definition of polygon states that they *are* flat, two dimensional. And by virtually every standard definition, polyhedra are finite figures. And 3 dimensional, too btw, so claiming the 2 dimensional tailings of the plain are polyhedra is simply absurd.
sir, this is a wendy's
@@LeoStaley he literally starts the video with the definition of what he considers a regular polyhedra, and gives clear explanations of why certain shapes fall under the definition whenever objections are possible (such as when he introduces apeirohedra or petrials). He emphasizes again and again that his answer is correct only under his definitions. I have no idea how he could possibly make it more clear.
@@TavartDukod he doesn't give a useful definion, and he later goes on to include figures which contradict his definition. Doesn't anybody watch videos with the slightest critical eye anymore?
@@TavartDukod and my point was that he should have made it clear that his definition was well outside the accepted normal definition.
When a theoretical non-Euclidean shape gets acknowledged before you
*sad Kepler Solid noises*
Have you seen jan Misali on the 48 regular solids?
@@qwertyTRiG 90% sure me watching that video is why this one popped up in my recommended.
TRiG (Ireland) Yeah..... I did...
Hello there, fellow those-that-had-this-video-recommended-in-the-sidebar-after-watching-the-one-with-48-regular-polyhedra.
@@Adam-zt4cn Howdy!
1:51 Possessed Matt
+TheCheungDan Woosh!
Clearly Matt was breaking into the fourth dimension
+TheCheungDan dont you fins it weird that he said "witch" as it happened? *plays x-files music*
+Saul McShane His book taught him much, indeed!
I'm afraid he can't say the word "square" anymore without risking "parker-squaring" what he's doing.
(Meh. It's an almost funny joke.)
You know, if my maths teacher would just be half as enthusiastic about mathematics as you are, my classes would be a whole lot more fun than they currently are.
I don't know how I feel about calling the "hyper-diamond" the 4-D equivalent of the rhombic dodecahedron. Because the hyper-diamond is made up of triangles (actually octahedrons) , not rhombuses. But I do acknowledge they have similar properties.
You know. Both of those shapes are made out of bipyramids. 2-D bipyramid is rhombus and 3-D bipyramid is octahedron.
@@matstruija5670 are bipyramids*
@@aguyonasiteontheinternet578 2d pyramid is a triangle and bipyramid is two 2d or whatever dimension pyramids with connected bases.
Most people maybe think that connecting 2d pyramids makes a quadrilateral which is not wrong.
I would say that it is looking at it in a different angle.
Angle
I want to see his response to jan misali video
How about this: platonic solids are convex. Literally nothing Jan misali mentioned after the platonic solids is convex. He was just talking about strictly regular figures. Not to mention he was using incredibly non-standard definitions of both polyhedron and polygon. Skew polygons are polygons in exactly the same sense that stone lions are lions; they aren't. Polygons, by the core, standard, universally agreed on definition, are flat. And infinitely extending figures are not polyhedra either, they are closed shapes with boundaries. Nothing he mentioned after the Kepler-poinsot solids is even a polyhedron.
@@LeoStaley there is nothing in the definition of a polygon stating that it has to be flat. there is also nothing in the definition of a polyhedra stating that it can't be infinite :)
@@LeoStaley Misali was talking about regular polyhedra, which don't require themselves to be convex
also, i'm not sure if plato specifically said the solids need to be convex and this requirement wasn't tacked on later, its not as if he knew of non-convex regular polyhedra back then
you seem to think that just because the shapes were ridiculous then they don't count, but that's not how it works here, the definition needs to be very strict else they're fair game, and the apeirohedra are very much polyhedra while tillings are like a degenerate polyhedra, and he could go much, MUCH further, as the definitions of either the platonic solids nor regular polyhedra don't specify that the space has to be euclidean or 3-dimensional, only that the solid iself is 3d, so shapes that can only exist in hyperbolic space or are skewed into 4d space are fair game, i don't think they specifically exclude degenerates either, and a regular hexagon based polyhedron is possible, its just that it'd be a degenerate with a height of 0
@@phyr1777
There's no such thing as "The" definition of a polygon or polyhedron. Jan Misali used an elegant but nonstandard definition based solely on symmetry, but more commonly-used definitions do indeed require flat finite polygons.
@@EDoyl well that still would give any solid made from actual polygons, mainly the Kepler-poinsot polyhedra, the regular tilings, and the Petrie-coxeter polyhedra merit. So there isn’t just 5 anyways.
"There are SIX Platonic Solids" Who else imagined Picard screaming that at a Romulan?
Nobody, he would scream it at a Cardassian
@@xTheUnderscorex indeed, my bad.
You drew on a book :(
+Ky Kanchuga With a pen?
+ISFiYIywAFIBc6qAIIIIIIIIIIIIIIIIQrXTJiCtY3Asd4WF But he wrote it so its ok
Yes, everything that I write is final.
No reasons for pencils, that's childs play.
And he found a remarkable proof that it is _the_best_ platonic solid, but there was not enough space in the margi
he drew on his own book, that he wrote, really he just edited it post publication ;)
4:07 it felt like it was attacking me
The Platonic solids are the five *strictly convex* regular polyhedra. There are more regular polyhedra than just the five platonic solids.
(Assuming a regular polyhedron is defined as a shape in 3d euclidean space which is face-, edge-, and vertex-transitive).
Matt, you, your channel, & your book are all amazing! :) I love Platonic solids & their 4D polychoron counterparts, as well as the many Archimedean solids.
Ooh yes, I'm a big fan of the Archimedean solids as well. The cuboctahedron may be my favourite.
:) Awesome! I think that my favourite Archimedean solid might be the great rhombicosidodecahedron. My favourite Platonic solid, however, is the wonderful dodecahedron. I'd have to say that my favourite Platonic polychoron is the commonly known, yet still beautiful, hypercube, though the 4-orthoplex (hyperoctahedron) comes close. Which is your favourite?
the d30 is pretty sweet. the number of sides is divisible by 1, 2, 3, 5, 6, 10, 15 and 30 so you can roll it and make most of the platonic die that way. you can roll multiple times multiplicatively to make a dice with n sides so long as n is solely divisible by the primes 2, 3 and 5. That includes the d4, d6, d8, d12 and d20 all in one dice
What about d120?
120 is divisible by 4, 6, 8, 12, 20
Just because there are other shapes that can make dice. Doesnt mean that every single shape "qualifies".
@@moondive4ever I was talking about simulating the probabilities of other dice using the d30. Roll a number mod x, where x is a factor of 30, and for dice that aren't factors of 30 (d8 for example) you can take the d30 mod 2 and roll 2^0, then 2^1, then 2^2 (where 000 can act as 8). The d30 is the smallest dice possible, both mathematically, and by shape, that contains prime factors of each platonic solid
@@ValkyRiver d120 absolutely works, and same for d60
It could also function as a D10 but that's not even an archimedean solid, let alone a platonic solid
those look trippy... probably because you drew 4d objects on a 2d canvas...
Well how he is depicting those 4d shapes is by illustrating their shadow; 3d shapes have a 2d shadow and 4d shapes have a 3d shadow, so we can't really see 4d shapes; however, we can see their shadow, that's why they appear to be " trippy ".
It's actually still 3D, just rotating in the fourth dimension, like a 2D slice of a 3D cake.
Jaguar Playz these are not slices of 4d objects but rather 4d objects projected onto a 3D space which was then projected onto a 2d space.
can we get an update with the full 48 ? :•P
ive seen that video aswell, whcih means this video is LACKING!
yes Yes YES YES
No, because none of those additional "polyhedra" Jan misali mentioned were convex, which is a required for platonic figures.
@@LeoStaley what is convex
@@MonsieurSwag basically, none of the outer faces can "see" any of the other outer faces, or if you're on the inside, you can "see" any other face from any face.
Jan misali is just thinking, "if only..."
So that why
"I am 4 parallel universes ahead of you!"
D&D player, just going "d4, d6, d8, d12, d20"
d10
d14
The sixth platonic solid is the d120
Imagine all the 4D dice tho. you got a 5d, 8d, 16d, 24d, 120d, and 600d.
@@Leonardo-G Just imagine rolling a 1 on a d600, or that one time you rolled a critical on your D600, immediately ascension to Godhood....
The 4 Kepler-Poinsot polyhedra are every bit as regular as the Platonic solids. Also the 3 regular skew apeirohedra if we include repeating finite Euclidean spaces and not just the standard infinite one.
I've noticed that the 5 Platonic solids have dualities that are very similar to the dualities of the 5 string theories. The heterotic SO(32) and the heterotic E8xE8 are dual, the type IIA and IIB are dual, with the type I being dual to itself. I don't know if this has any significance, but it's interesting.
d4
d6
d8
d12
d20
Dungeons & Dragons taught me geometry
The icosahedron will always be linked to rolling for initiative.
You find yourself in a 4 dimensional dungeon with 4D monsters. You could do a perception roll but no matter how high it is you will never be able to perceive the fourth dimension because you aren't a hyperspace alien
+standupmaths Actually, that depends on which edition you're playing. The Frank Mentor "Basic" D&D from the 80's used a d6 IIRC and 1st and 2nd edition of AD&D used a d10, which is an interesting grey area since the true d10 is non-Platonic but originally a double-labeled icosahedron was used.
+Antenox So now there is a need for 4dimensional dices. Just to make you learn this video. Right?
Well, what will we roll with a hypericosahedron??? I mean it has to be something that goes from 1 to 1200... Luck of some sort, perhaps.
It must be boring to be a 10d being thought. So little regular polytopes for dices...
VeteranVandal
That's for what we call "D&D Epic Level Adventures"
Thank you. Your enthusiasm for maths invigorates my own!
I would have said the square is a regular quadrilateral, not a regular rectangle, to be consistent. But I'm a bad guy. ;~)
That's what I would've said too. In maths everything has like 3 or 4 different names.
You crazy quadrilateral people.
+TyYann A square is a special case of: a polygon; a quadrilateral; a kite; a trapezium; a parallelogram; a rhombus; a rectangle. There are probably other things I've missed in that list...
+Josh Lovasz
If we really wanted to be consistent we should call them either:
- triangle, tetraangle, pentaangle, hexaangle..., or
- trigon, tetragon, pentagon, hexagon..., or
- trilateral, quadrilateral, pentalateral, hexalateral...
+adb012 nobody wants to be consistent
48 regular polyhedra smh
1:52 I’m convinced you’re a glitch In the system
Why do the vertices of the hypertetrahedron and hyperoctahedron like to slap me in the face so much?
Awesome job on the animations! Very professional. Keep up the great work Matt.
Thanks! I probably spend longer on the animations than I really should.
+standupmaths you spend the right amount of time, to make each one look brilliant. You care about quality and it shows, and we love you for it.
Just found this randomly when looking into platonic solids. This isn’t a platonic solid, platonic solids are regular polytopes in 3 dimensions this shape only works in 4-D.
He probably should have said Platonic analogue
It’s a 4-D polytope
It is a platonic hypersolid.
The technical name for those is "Convex regular 4-polytope". Calling them "4D platonic Solids" is a lot nicer IMO.
@@Inversion10080 you don't get to make up language just because it sounds nicer. "Cold" sounds better than "Hypothermia" but they're not interchangable.
The video title is very misleading. By definition, a Platonic Solid is... A solid. Anything bigger would be considered a polytope, not a polyhedron.
@@metachirality “polyga”
:unknown:
A 2-solid. A 1-solid is a 2D shape, a 2-solid is a 3D shape, a 3-solid is a 4D space, and so on. Well, the "solid" he describes is a 3-solid, and not a 2-solid.
enjoyed this and I may purchase your book kind sir
The hyper-diamond could also be seen as a 4D cuboctahedron
0:38 it’s a regular quadrilateral. Technically
Oh
03:30 thats actually really fucking cool
gotta get myself a floating rhombic dodecahedron someday
The floating type are really expensive.
nice pfp
Thank you so much. That was beautiful!
I understood very little of this, but it's incredibly fascinating. Thank you for sharing!
I'm just happy that someone even made a vid about the 24-cell at all, and I'd never heard of it referred to as a hyper-diamond.. which I prefer now, as 24-cell sounds too much like.. a really cheap prison ; P It's like they named the shape in honor of the antithesis of it's true function. "Hyper-diamond" finally liberates it : )
Only 6 Platonic Solids? Maybe back in 2015. Everyone know there are 48
Jan misali was ridiculously incorrect with that video. Not to mention the fact that platonic solids are explicitly convex. He was using a completely nonstandard definion of polygon (yes, they do have to be flat, two dimensional), without informing his audience that he was doing so.
@@LeoStaley jan Misali never said those 48 were Platonic solids though.
@@LeoStaley jan Misali said *48* polyhedra, not platonic solids
@@sushi-mayo except that nothing he described after the Kepler-poinsot solids was even a polyhedron. A polyhedron, by definition, is 3 dimensional, so it is absurd to claim that a 2d tiling of the plane is a polyhedron. There are some contexts where some mathematicians use polyhedra to refer to other figures even above 3 dimensions, but none of them would include any 2 dimensional figure like a tiling of the plane. Later, he claims that a polygon doesn't need to be 2 dimensional when that is in fact a core part of the definition of polygon. Skew polygons are not actual polygons any more than polyhedra are polygons. They are a generalization of the idea of polygons in much the same way that polyhedra themselves are a generalization of polygons.
And notice, people, that this very comment we're replying to proves that people misunderstood the scope of Jan's video, which isn't surprising, because of the way he framed it.
I just read the very same chapter today, what a coincidence!
I love your book so far!
I hope you enjoy the second half as much!
I surely will. You have a great sense of humour, very punny!
First of your vids I've seen, gonna continue on and check out your lecture @ R.I. and your book looks raaad : )
What is your opinion on the
stellated dodecahedron?
The great icosahedron is the best regular polyhedron. Fight me
@@Choinkus i'm more of a great dodecahedron guy myself
There are four lights!
BraneBrain
Hella. It's pretty intense and a great character exploration of Picard.
+DrRawley it's a rip off from George Orwell, but I'm not dissing it.
+DrRawley Great reference, but how does it apply to the video?
Denis Lipatnikov
I had just watched that episode of star trek the previous day, so it was the first thing that came to mind. a bit of mirth if you will.
+DrRawley you sir are the greatest man to have ever lived.
The orthographic projections look amazing. Makes me think of the whole sacred geometry stuff.
I'd love to find versions of them without all the solid circles, maybe make a carpet with the design or something.
Great video. Do you have videos that go into more advanced and detailed stuff. I'm 16 and I love the fourth dimension. I got interested in it at the age of 13 when I noticed geometric patterns with shapes and stuff and I only found you recently. I love your videos.
I like to think about 3D->4D by comparing it to 2D->3D and 2D->1D, doesn't take a lot of prior knowledge to come to conclusions about it. For example, hyperspace beings could see inside us, just like we could see inside 2D beings on a plain, if we see them from above.
Try it! :) Just remember 4D's not supposed to make any sense for our 3D brains...
Flatland.
Cryp Tic yes.
try analytic geometry. These 4d images are generated by these methods, and it isn't even that hard
Rotations in 4D? I will use stereographic coordinates.
See inside us... pretty kinky
"There are only 5 regular polyhedra"
jan misali: Am I a joke to you?
All platonic solids are regular polyhedra but not all polyhedra are platonic solids
That hyper-icosahedron looks amazing!
It is the best indeed. I have a puzzle similar to a rubiks cube called the curvy copter. It’s a cube shaped puzzle based on the rhombic dodecahedron and the various ways it turns make for the most fun puzzle i have ever solved
How does the hyperdiamond get to be a Platonic solid if it's not made out of regular polyhedrons?
it does and it is! regular octahedrons.
Face polygons aren't regular
But I guess the faces where the octahedra join are not themselves polygons, yes? So it is still a bit different to the other 4D "platonic solids" yes?
I love this channel! Just bought the book (in store, didn't know you sold them as well).
BTW, I love the song you use, can I get it somewhere?
+FrederikMeynen I want that song as well.
Yes, I wanted to sell them myself so I could sign them for people. The song is my theme song and currently not available anywhere!
+standupmaths PLEASE make it available for purchase!! I love the standupmaths theme song!!!
I love this guy's intro and the 4th dimension
your channel never bores me.
I laughed every single time!!
Great to hear! Hopefully I'll keep you laughing at such a predictable rate.
1:39
We can call that "Platonic Love" then? =P
+Mohammed Zaid booooooooo
Kremlit the Forg
:(
+Mohammed Zaid
But there's only ONE true parabola
Cool fact: Half the 4D Platonic solids can tile 4D space. (the hypercube, the "hyper-octahedron", and the hyperdiamond)
I love the amount of videos lately :)
Thanks! I'm trying to put out regular videos. It just takes a lot of time.
standupmaths Oh, and could you make something about right triangles with equal area and perimeter? Might be below the level of the videos, or just not interesting enough, though...
YOU DREW IN YOUR BOOK! Well I guess someone will want it.
I wrote it: I can draw in it!
I love the hyper diamond. I want one. But I don't live in the fourth dimension. Yet.
Maybe you do live in the 4th dimension.
If you were 2D how would you know you don't live on a cube?
epsleon We live in eleven dimensions.
@James: indeed.
***** I was waiting until someone got that physics joke.
in 4d galaxies would not be able to form and would remain as dust clouds
Beautiful ; of this world but not of the world; how lovely!
I dont know why these are so beautiful especially how they dance !
You make me audiofobic with this noise you use in the back/foreground.
viewer cant believe nor understand the hyper-diamond. He screams Geometrically
Hyperdiamonds are a girl's best friend...
@@maxnullifidian You mean SuperGirl's best friends....
But... but... you wrote in a book!..
It's his book tho
oh my days, this is awesome!
I saw a hyper diamond (or rather the best representation of one we can make) the other day, and I was awestruck by it 🥰
> "watch my Royal Institution 4D lecture"
the lecture wasn't 4D :p
Well, the 4th dimension (and the 3rd dimension) were folded up so small that you couldn't see them.
+Joe Holland Time isn't the fourth dimension. Relativty says that time dimensions are seperate from spacial dimensions, so the 4th dimension != time.
+William Rutherford Time is the fourth dimension but not the fourth spacial dimension.
+appleturdpie it was a math video. He was talking about 4D shapes. That means he was talking about space, not time.
+appleturdpie Well.. It's one of MANY dimensions. Sure, you can CALL it the fourth dimension. I could also call the Y axis the "fourth" dimension. Or perhaps time can be the first dimension. What I'm getting at here is that the labels "first", "second", etc, are entirely arbitrary.
you forgot the best part about the rombic-dodecahedron: it tesselates the space! not sure about the hyper-variant, though.
A rombic-dodecahedron is not made of regular polygons in 3D
The rhombic dodecahedron and all higher omniaugmented hypercubes tile space, since you can decompose every other cube of the ordinary cubic honeycomb into pyramids and glue them onto the remaining cubes.
Great presentation 👌👍🥰
I would make these as models built of drinking straws and fishing line, suspend them, and shine a flashlight through them as they spun just to see the shadows play😉
2:39
ER MER GERD
I'm such a fanboy of that shape.
Seriously, I've done many an evening reading up on it and whatnot.
me, who just watched a video about 48 platonic solids:
pff pahetic
Is so painful that I have to keep correcting this stuff. Nothing Jan misali mentioned after the first 5 platonic solids is a platonic solid because none of them are convex. Plus, he was using wildly non-standard definitions of polyhedron *and* polygon.
there was only ONE section in that video about platonic solids.
You should collaborate with Trey Stone.
Funny guy ...
That took me a while. Jesus Christ...
The correct representation of the symbol for infinity. Very subtle ;-)
REGULAR TETRAHEDRON: 4 triangular faces,6 edges,4 vertices
REGULAR HEXAHEDRON: 6 square faces,12 edges,8 vertices
REGULAR OCTAHEDRON: 8 triangular faces,12 edges,6 vertices
REGULAR DODECAHEDRON: 12 pentagonal faces,30 edges,20 vertices
and... THE REGULAR ICOSAHEDRON: 20 triangular faces,30 edges,12 vertices
The Rhombic Dodecahedron is one of 13 Catalan Solids. Each face is a rhombus.
the fifth beatle is clearly yoko ono
Wow... nice clickbait. I thought this definition assumed 3D euclidean space. However, there are 48 3D euclidean regular polyhedra, not 5.
Jan misali was wrong. He was using non-standard definitions for both polyhedra and polygons. Polyhedra are 3 dimensional, so 2d tilings of the plane don't count as polyhedra by anyone's definition. And the definition of polygon *does* define them as flat, 2 dimensional figures. Skew polygons are polygons in the same sense that stone lions are lions; that is, they aren't. And polyhedra are composed of polygon faces. Literally nothing he mentioned after the Kepler-poinsot solids was actually a polyhedron.
Where can I find your outro song? I absolutely love it and would love the hear the whole song.
Use the app shazam to find the song
The rhombic dodecahedron is the dual of the cuboctahedron which is not a Platonic Solids but the building block of the twelfth ffellonic form.
Sometimes to much attention is placed on the vertices, faces and edges of polyhdera rather than the axes they describe.
What song is that at the end?
+Icaro Vasconcelos Darude - Polygonstorm
That is the Stand-up Maths theme song!
+standupmaths, it reminds me of the Super Hexagon a bit.
+standupmaths Is there a place to download / buy this song? :)
STOP SPOILING UR BOOK! I'm planning to get it this Christmas dammit!
+Jack Drewitt Don't worry, there's lots of stuff in the book that isn't on his channel yet :)
Spoiler: I talk about prime numbers as well!
+Jack Drewitt Or did you mean by writing on it, cos it killed me to see him scribble on the lovely page.
I don't care if it was for a promotion, and he wrote the book. Christ, I don't even care if he soaked and crushed the papyrus himself then set the type by hand, it's just wrong to write in anything with an ISBN number.
stalfithrildi no i didnt mean that, altho i can sort of see where ur coming from
+stalfithrildi
But you're okay with people doing it in books that predate ISBNs? Also, isn't "ISBN number" redundant? =P
That last bit got me haha
I wish I could see a glance of the actual fourth dimention :c
0:53. Very smooth, mate. Bet you're proud of that.
More than I am prepared to admit!
+standupmaths Lovin' the videos; you're on a roll! Keep them coming (please).
+Adam Duncanson I'm trying! The only problem is finding enough time.
Nah, sixth one is the teapotohedron. :)
Utah
"in the fourth dimension"????? NO NO NO!!! It is "in four-dimensional Euclidean space". You cannot pin down a "fourth dimension" just as you cannot pin down a "third dimension" in the 3-dimensional Euclidean space.
+subh1 Sure you can. z is the third dimension. w is the fourth. Completely arbitrary, of course, but still can be useful.
Yeah, that's what I said, sodium chloride
As 2D objects require 3D spaces to represent, and 3D objects require 4D spaces to represent. Since we have a "third dimension", we can use the fact to prove we are living in 4D Euclidean space. If we were living in 5D Euclidean space, we would have a "fourth dimension", and the Flatlanders are living in 3D Euclidean space.
I have that book! Woo.
“4th musketeer”
“5th beetle”
“6th tally hall member”
At 1:52 there is a glitch
“which”
BRUH THERE ARE 48 REGULAR POLYHEDRON LOL GET GOOD GIVE ME UPDOOTS
Not convex. Jan misali never pointed that out, nor did he mention that he was using a totally nonstandard definition of polygon. The standard definition *does* require that they be flat, in 2 dimensions.
You mean 49 cus 5 plus the 43 from Jan miseali and 1 from here
4:06 also pentachoron, regular tetrahedral pyramid, regular 5-cell,4-simplex
4:15 also tesseract, regular cubic prism, regular 8-cell,regular octachoron,4-hypercube
4:21 also hexadecachoron, 4-orthoplex, regular 16-cell...
4:24 also hecatonicosachoron,regular 120-cell
4:39 also 600-cell, hexacosichoron
I know this is a really old video, but there is a new game demo out of a 4D version of Minecraft called 4D miner and its amazing! It's still in development but you should check it out by a guy called Mashpoe 👍
As much as I love Matt Parker (I've even bought his book) I really don't like some of his nomenclature. Not because it doesn't sound cool, but because it's actually very misleading about why the various geometric figures exist in the ways they do.
So I'm afraid I'm going to have to make a long and critical comment about it.
Let's start with the video title. There are FIVE platonic solids. Platonic solids are 3D, because /solids/ are 3D. From Wikipedia, for example: "solid geometry is the traditional name for the geometry of *three-dimensional* Euclidean space".
Platonic solids are also known as regular convex polyhedra. The equivalent in 4D is "regular convex polychora". Or in general, you have n-dimensional "regular convex polytopes". "4D Platonic solids" doesn't make sense because that's like saying "4D 3D regular convex polytopes".
If you want to say there are six regular convex polychora, go ahead and say that. Don't say that there are six regular convex polyhedra ( = Platonic solids), because there aren't.
Now, moving on. Hyper-diamond? Sure, you can cut up bits of a tesseract and reattach them to make an icositetrachoron (or 24-cell), and sure, that makes an interesting link with the rhombic dodecahedron, but the 24-cell doesn't have a single rhombus on it. Its faces are triangles and its cells are octahedra. There is no resemblence to rhombi.
Let's have a gander around 5:10. "Icositetrahedron?" No, it's not often called that. There are various icositetrahedra, but those are different figures, and they live in 3D anyway, as the name would imply. The name you wanted is the /icositetrachoron/. As for Octacube? *googles*... The only reference I can see for that one is as the name of a sculpture representing the figure. And, sure, "hyperdiamond" appears on Wolfram Mathworld, but it's completely unreferenced.
Also, 3:55... What's a "polytshorron"? It's from Greek, so it's pronounced with a hard ch / k sound. Polychoron. Look it up on Wiktionary if you like.
Just to be clear, I've got no issues with names like the "hyperoctahedron", they're a bit of a mouthful but are accurate, since "hyper-" just means "higher dimensional analog of". Heck, "hyperdodecahedron" is probably easier to understand than "hecatonicosachoron", and definitely easier to remember, but my dislike of that series of names is neither here nor there. (I'd previously concocted my own nomenclature to deal with this too, but really I'm in no position to start talking about that, if you really want to know about it, you'll know where to find it.)
Okay, I'm done. I'm probably going to get a million down-votes, but I'm not just going on a rant for the sake of it. I really like Matt Parker's work, I just wish he would do a little more research on the words he's using before teaching them to everyone else.
+Keiji Ikari lol no one knows how to respond to that.
What are you, Asian?
+AbuJafar Choudhury I'm British for the record.
»lol no one knows how to respond to that.«
+Ayyy Lmao Well, maybe because there's simply not much to add to it.
It's on point, informative, and manages to be very critical analyzing the video's faults while staying humble.
I personally agree wholeheartedly with +Keiji Ikari's concerns about Matt's somewhat negligent use of terminology, and would consider it the best comment in this whole comment section even.
same
There's actually 7 platonic solids, the sphere is a one sided platonic solid.
apparently not for some reason, it's a bit like saying 1 is a prime number.
I believe it's because there are no faces, vertices or edges to be identical to one another, thus making it not a polyhedron, which I believe is one of the qualifications for being a platonic solid.
*Polyhedron*
- Only planar faces need apply.
That's like saying a circle is a polygon, it isn't, poly means many and 1 isn't many
If you think about it, a sphere is the limit of a regular infinihedron. At least, that's the only way I've been able to get it to make sense.
those 4d platonic solids look qutie trippy
One of the rules of Platonic solids is that they must be in a 3 dimensional, Euclidean space.
5:30 - Matt, we can see the string!! :D
Can you do a video about Archimedean,Catalan and Johnson solids?
An unobstructed Garnet Crystal will grow into a Rhombic Dodecahedron. They look amazing. After watching this I love mine even more now.
love them !
“In fact, I’ll highlight it right now”
*draws a rectangle
My son found a cute magnetic shape toy. I noticed it had all the same sides (Diamonds). We were trying to figure out which Platonic Solid he was holding. Your video revealed we were looking at the Rhombic Dodecahedron.
Is there an electronic version of your book? :3 as awesome as it would be to hold a solid copy, i wont be able to have a bookshelf for quiet a while
I don't understand those 4D shapes.. maybe I need to get your book to get it o.o