The Five Compound Platonic Solids

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Do check out my video with Adam Savage over on Tested: • Can Adam Savage and Ma...
Yes, I'm back in NYC for An Evening of Unnecessary Detail on Sunday April 14. www.eventbrite.com/e/matt-par...
Pre-order my new book! mathsgear.co.uk/collections/b...
The excellent graphics of spinning dodecahedrons were made by Ben Sparks. You can see the GeoGebra file here: www.geogebra.org/m/yhkepkbc
Some more details about space diagonals on Math Stack Exchange.
math.stackexchange.com/questi...
Huge thanks to my Patreon supporters. They keep my polyhedra intersecting. / standupmaths
CORRECTIONS
- None yet, let me know if you spot anything!
Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Laser cutting by Lisa Mather
Extra graphics by Ben Sparks
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
Training on using a bandsaw by Adam Savage
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...

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5 мар 2024

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Комментарии : 749

@orbitalshawn0625 2 месяца назад

I love dodecahedrons but our relationship will always be platonic

@Elesario 2 месяца назад

Groan... but also cute.

@frba9053 2 месяца назад

Perfect pun

@idontwantahandlethough 2 месяца назад

nice

@greanbeen2816 2 месяца назад

What a shame, I thought things were just golden.

@abstractapproach634 2 месяца назад

That would break plato's heart, he thought the dodecahedron would always be your everything

@LSA30 2 месяца назад

D I A G O N A L S I N S P A C E

@aiocafea 2 месяца назад

sadly youtube bitrate compression messes with my full enjoyment of D I A G O N A L S I N S P A C E

@Zi7ar21 2 месяца назад

🛸👾

@Yezpahr 2 месяца назад

It is just a blatant theft from Science Asylum, but I'm not even mad. Well done by Parker-man.

@victormunroe2418 2 месяца назад

@@Yezpahr nah, clearly it's blatant theft from The Muppets

@FLPhotoCatcher 2 месяца назад

I'm sure Adam Savage is a man. I'm tired of the misuse of my language by an elite few, who are trying to spread the misuse.

@qwfp 2 месяца назад

4:29 ϕ×ϕ this is my new favourite emoticon!

@JavSusLar 2 месяца назад

Fun fact: by definition, φxφ=Φ+1

@mySeaPrince_ 2 месяца назад

🤯

@5ucur 2 месяца назад

фхф

@felicityc 2 месяца назад

ϕwϕ classic cat eyes

@onebronx 2 месяца назад

¯\_(Φ×Φ)_/¯ - PARKER DIAGONAL IN SPACE!

@UnicornPowerzez 2 месяца назад

the autotuned "but i couldnt be bothered" cracked me up, this is why matt is the best

@kbsanders 2 месяца назад

1:31 Alex, do you want to give me a hand with this? Alex: Sure Caption: No

@thomaskaldahl196 2 месяца назад

made me think I was insane since I had to scroll so far to find this 😭

@2ndfloorsongs 2 месяца назад

Shamelessly stolen from Jean-Luc Godard.

@robinsparrow1618 2 месяца назад

@@2ndfloorsongs who?

@2ndfloorsongs 2 месяца назад

@@robinsparrow1618 Jean-Luc Godard was a famous French filmmaker. One of the many things he was noted for was having English subtitles that were frequently different from the spoken French soundtrack of his films. These were not slight differences in the translation, they contained different storylines, conversations, and descriptions of what was happening. They were frequently written by literary authors he'd invited and they were told just to view the movie and write their own script that went along with the visual film and not to worry about what the original French film was about. He was a legendary innovator and invented the "jump cut" film transition among many other things. I didn't mean to imply this was actually stolen, this was meant as a humorous joke.

@robinsparrow1618 2 месяца назад

@@2ndfloorsongs oh ok, this is actually really interesting and cool to know about. and it's a good joke with this context, thank you

@gallium-gonzollium 2 месяца назад

The “Diagonals in SPACE” interjection might be the best highlight for this channel in a while. And I’m glad to be a part of it when it becomes a happy meme. :)

@NoNo-nr2xv 2 месяца назад

I have heard on the grapevine they are making a film as a sequel to snakes on a plane. DIAGONALS in Space. Samuel L Jackson "I don't care if they are cubes in a compound tetrahedron, I am fed up of these god damn mother flipping DIAGONALS IN SPACE"

@falfires 2 месяца назад

Matt still trying to make us forget about the Parker Square. But we will never forget. :D

@richbuilds_com 2 месяца назад

I was expecting a more Piiiiigs iiiiiiin Spaaaaaace vibe.

@MasterHigure 2 месяца назад

Clearly Science Asylum inspired, if you ask me. Not that I'm complaining.

@zeotex2851 2 месяца назад

The quiet echoey "space" at 3:45 killed me 😭😭😭💝💝💝

@Elesario 2 месяца назад

My condolences to your family.

@zeotex2851 2 месяца назад

@@Elesario than you, its so sick how you still have access to RU-vid in the afterlife, didn't expect that 💝💝💝

@aMessvv 2 месяца назад

Was about to comment this hahaha great attention to detail

@dummyaccount1706 2 месяца назад

I see that VFX department got a raise recently

@tsawy6 19 дней назад

Timing department getting their budgets slashed

@HunterJE 2 месяца назад

Great job on emulating the old educational film aesthetic for those insert animations, really sent me back...

@gormster 2 месяца назад

I think a reference to Look Around You

@andreasbaus1554 2 месяца назад

It reminded me of the animated sequences from the classic BBC Hitchhiker's Guide to the Galaxy TV series

@stevewithaq 2 месяца назад

4:42: maybe tropic would be a better word than equator, as there are two of them parallel and equidistant from the central plane.

@nxpnsv 2 месяца назад

Excellent. I especially liked the D I A G O N A L S I N S P A C E.

@taureon_ 2 месяца назад

12:00 a good excuse for drawing 12 pentagrams on a dodecahedron

@rsyvbh 2 месяца назад

Matt is summoning something in the exact center of the dodecahedron so that he can trap it

@atmatey 2 месяца назад

Fun fact: Both the small stellated dodecahedron and the great stellated dodecahedron can be thought of as 3D versions of a pentagram. They are both very cool shapes.

@nicholasvinen 2 месяца назад

All hail Satan^12.

@frojojo5717 2 месяца назад

@@atmateywell, duh! How else would you trap a demon in the centre?

@NoNeedForRandomNumbers 2 месяца назад

Oh god the SFX budget went sky high for this video!

@aikumaDK 2 месяца назад

One might even say it is IN SPACE

@imaginaryangle 2 месяца назад

If you want Steve's subscribers, you need to fill that thing with water. You were so close! 😄 I really dig how your personality and style come through even in the bits other people help you with these days. Been a fan of yours for many years, you always bring me smiles, quite a few belly laughs and a ton of inspiration

@PeterFreese 2 месяца назад

I was not prepared for the joke at the end. Well done.

@GoranNewsum 2 месяца назад

Ben: Hey Matt! I've made a spinning dodecahedron in Geogebra! Matt (after this video): I don't need you anymore! I can make my own spinning polyhedra!

@dysphoricpeach 2 месяца назад

13:34 the convex hull of the 5 octahedron compound is the icosidodecahedron. I know this video is about regular dodecahedrons, but I was a little sad when you brushed it off. It’s my favorite compound, my favorite stellation, and my favorite faceting. It also looks a whole lot like my one of my favorite polyhedra, the disdyakis triacontahedron!

@galoomba5559 2 месяца назад

The icosidodecahedron _is_ its convex hull. I don't know what Matt was talking about, maybe he meant that the convex hull is not regular.

@columbus8myhw 2 месяца назад

@@galoomba5559It really sounds like he accidentally skipped a word.

@DaxSkrai 2 месяца назад

Everyone taking about "diagonals in space" but 11:41 is the best voice sample for an EDM song.

@wyattstevens8574 2 месяца назад

And what about the "but I couldn't be bothered" from 7:47?

@asheep7797 2 месяца назад

@@wyattstevens8574they couldn't be bothered to mention it

@ps.2 2 месяца назад

Hot take: _Howard Carter's entire soundtrack_ for Matt's entire channel is, like, the only _good_ EDM I've ever heard.

@terdragontra8900 2 месяца назад

The cube dodecahedron relationship is like, my favorite thing about 3d geometry, its so beautiful

@needamuffin 2 месяца назад

Mine is the three orthogonal golden rectangles forming the verticies of the icosahedron.

@terdragontra8900 2 месяца назад

@@needamuffin oh yes, in fact, that is also a result of same connection between the symmetry groups. (the icosahedron is duel to the dodecahedron, and three orthogonal planes have an associated cube)

@estherstreet4582 2 месяца назад

Every d12 I own (which is 2, I'm not a weird dice hoarder) has the cube shape drawn on in sharpie, it's so satisfying to look at. I also like how the pieces you'd have to "cut off" to make the dodecahedron into a cube are shaped like little rooftops.

@HunterJE 2 месяца назад

The smaller solids left behind by the shapes discussed are super satisfying in their proportions too, both the sort of flattened, obliquely truncated triangular prism you get from cutting along the square/cube and the frustrum of a pentagonal pyramid cut off by the near-equatorial pentagon...

@jace.miller 2 месяца назад

I like several of the integrated shapes. Discovering the square within the dodecahedron reminds me of the end of this demonstration of the Cross Sections app: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2uHfFp1XCPc.html

@Nebula_ya 2 месяца назад

7:43 It's the "Parker Fluorescent Embedded Cube", he's done it again!

@superj1e2z6 2 месяца назад

I couldn't be bothered marking the insides translates to "I gave it a go". Totally a parker cube.

@emperorbless120 2 месяца назад

Matt Parker: "There are 5 regular polyhedra." Me, a jan Misali enjoyer: "there are 48 regular polyhedra"

@robinsparrow1618 2 месяца назад

8:00 the rotation due to parallax and the actual rotation cancel out briefly. very cool to see

@patrycjar1026 2 месяца назад

You should be honest - "You might know me from Numberphile video with the Parker Square"

@awebmate 2 месяца назад

The first time Matt had a collab with Adam, he referred to him as "Adam Savage from Mythbusters". In return, Adam Savage referred to Matt as "Matt from Numberphile".

@CBWP 2 месяца назад

Adam was with mythbusters. Matt isn't with numberphile...

@Artaxo 2 месяца назад

Are you THE Matt Parker from the Parker Square? What an honor!

@andynicholson7944 2 месяца назад

8:32 it tickles me no end to learn that Matt is a Look Around You fan

@ironpro7217 2 месяца назад

8:24 matt's mental maths is on point

@walderlopes3372 2 месяца назад

Oh, yeah! I have Steve's last video on the "watch later" list but I always forget that list. Thanks for reminding me, Matt!

@andrewkepert923 2 месяца назад

Correction: graphic at 4:22 is longest diagonal = φ √3.

@robinsparrow1618 2 месяца назад

replying to boost the correction

@Zejgar 2 месяца назад

The dodecahedron is slowly de-throning the icosahedron from being my favorite platonic solid, thanks to crazy fun stuff like this.

@davidioanhedges 2 месяца назад

"Lots of ridiculous maths things" .... is possibly the best description of this channel I have heard ....

@jace.miller 2 месяца назад

Discovering the square within the dodecahedron reminds me of the end of this demonstration of the Cross Sections app: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2uHfFp1XCPc.html Let me know if a tool like that could aid in visualization. You could possibly do a follow-up on the hexagon within the hexahedron.

@paulzagieboylo7315 2 месяца назад

4:25 This diagram is the longest space diagonal, not the medium-sized one Matt is talking about in this segment. But the length (phi^2 = phi + 1) is correct for the medium-sized one!

@Peterwhy 2 месяца назад

Thanks, I paused and looked for this comment.

@user-wj7rq2ny2p 2 месяца назад

phi^2 = phi + 1 Golden ratio quadratic equation.

@gnothisauton2116 2 месяца назад

There is something SO satisfying about those taped models. Thank you.

@jeffclarke3191 2 месяца назад

This was so much fun to watch and in my opinion one of Matt’s best in terms of pure enjoyment and entertainment. Matt’s enthusiasm is totally infectious and a delight to watch. The brilliant choice of music only added a new dimension (!) and I cannot praise this video enough!

@agrajyadav2951 2 месяца назад

agreed

@olgastec-mitura3890 2 месяца назад

I love the over-the-top editing style.

@Reprint001 2 месяца назад

Just goes to show how you can't please everyone. I hate it.

@deliciousrose 2 месяца назад

7:40 this is next level editing XD

@babilon6097 2 месяца назад

One thing to do would be to also tape the insides, but wait, there's more... you could have taped each cube with a tape (or drew with a marker) that reacts to a different wavelength of UV. Then by switching different blacklights you could switch between the cubes instead of having them on all at the same time.

@TheGreatAtario 2 месяца назад

Are we sure there is such a product?

@redoxxed 2 месяца назад

I absolutely adore the visual representation of the see through dodecahedron with the tape to show the square, pentagons etc! it's just such a satisfying visual proof of the lengths of the space diagonals

@milandavid7223 2 месяца назад

I had to make a geometric solid out of paper as a highschool project. I chose a dodecahedron and it was pretty wild finding out that the whole net can be constructed (with straightedge and compass) using just a unit side and like 3 or 4 powers of the golden ratio. Imagine unfolding one half of the dodecahedron into a flower shape. That flower is bounded by a pentagon that's phi^2 larger than the faces.

@MrDivinity22 2 месяца назад

Once again, you're knocking it out of the Parker with these videos!

@EdHarrisonMusic 2 месяца назад

Great to see you cover this, I adore the dodecahedron and its properties. I'd love to see you explore the geometry of DNA!

@daniwalmsley611 2 месяца назад

6:45 the coolest part of this was that this was wholely unsurprising thanks to your previous videos on the rhombic dodecahedron It's lovely when one maths investigation is helpful in understanding a completely unrelated one

@bizm 2 месяца назад

Matt, you are honestly a master educator. I'm in my thirties and failed nearly every math class I ever took (and whatever I did manager to learn, I promptly forgot when I graduated high school). Every time I watch one of your videos I learn something and I'm able to truly understand and retain concepts that boggled my mind before.

@kelseyfassett7099 2 месяца назад

the editing on this is impeccable

@qwertydragon8385 2 месяца назад

Matt thanks for running the only math channel I've found that will always explain things in a way that makes sense and makes me laugh every time! I've been watching your videos for a long time and you've only gotten better with time!

@arxaaron 2 месяца назад

When I started learning 3D modeling and animation on the Amiga circa 1988, one of the bigger challenges I set for myself was modeling and animating regular pentagonal dodecahedron with a raised star on each face (similar to the Chrysler logo) -- thus the dodeca-deathstar was born. A couple years later, working in high end video post production, I used the mathematical precision of the amazing Ampex digital optics device with a precise pentagon matte to layer a spinning dodecahedron with different video on each face -- calculating exact angles and depth offsets with an HP-15c calculator was a wonderful challenge that grew my maths skills considerably. Sorry Matt, but the platonic dodecahedron is, and always will be, the BEST dodecahedron.

@andyb9124 2 месяца назад

That's a lovely, easy to visualize, and excellent way to explain these conceps. Absoulytely a great example of how to teach a concept really well. Good job, Matt.

@jajssblue 2 месяца назад

3:30 I immediately know where this video is going and I love it!

@crawley6957 2 месяца назад

@12:53 seven swans a-swimming, six geese a-laying, FIIIIIVE INTERSECTING CUUUUBES

@Schambes 2 месяца назад

I love your visualization, it makes the whole thing insanely well understandable for me

@ZedaZ80 2 месяца назад

This was such a good visual demonstration!

@Zenzicubic 12 дней назад

I've always loved the regular compounds and their beautiful symmetry. When I built my first raytracer and figured out how to raytrace cylinders, the compound of 5 tetrahedra (which is my favorite) was one of the first things I made a render of. The regular compounds were the first things I printed when I first got my hands on a 3D printer. Great video as always!

@HereticB 2 месяца назад

the editing is amazing!!!

@Mr_Geo 2 месяца назад

Loved the book! I love how you were able to invent *time traveling* with trig! Mark my words, This is going to be the best-selling book in history!

@scv4236 2 месяца назад

The editing is genius

@ricdavid 2 месяца назад

I love the ones where you can tell how much fun he had with it, and also where the concepts don't fly too far above my head. Also I can see myself making a shitty scaled down version of this in the future.

@XplosivDS 2 месяца назад

Good ol' small stellated dodecahedron and the great stellated dodecahedron

@James-Calvin 2 месяца назад

I am excited for your new book!

@agrajyadav2951 2 месяца назад

your videos are capable of pulling one out of depression and make them fall deeper in love with mathematics. Thanks a lot for your work, sir.

@Audey Месяц назад

I almost audibly gasped when you taped that square on. This was a really cool way of showing everything, better even than a 3d animation or something I think.

@THESP-rz3hg 2 месяца назад

I aspire to enjoy my work as much as Matt

@mrautistic2580 2 месяца назад

This is one of my favorite Stand-Up-Maths video!!!!!

@smanni01 2 месяца назад

A masterpiece of maths and editing

@ffggddss 2 месяца назад

The compound polyhedron made of a pair of intersecting regular tetrahedra, is aka the "stella octangula." It was a favorite of Johannes Kepler, the guy who fiddled around with the 5 Platonic solids to try to explain the relative sizes of the planetary orbits, and the guy who formulated the famous "3 Laws of Planetary Motion" that bear his name. Anyway, the 8 vertices of the stella octangula are the vertices of a cube. Which also explains the 10 regular tetrahedra in the regular dodecahedron, once you've highlighted the 5 cubes in it. Fred PS. Also interesting to note, is that the main (longest) diagonal of an n-dimensional hypercube of unit edge, is √n.

@miallo 2 месяца назад

9:20 "The shape we were trying to made was the compound-5-intersecting tetrahedra. Here is a picture [...] and I've actually got a little print out over here" - am I the only one who was a bit sad that it wasn't a 3D print?

@charlesmarshall7045 2 месяца назад

Turning obscure math into real world objects, keep up the good work Matt!

@dajac Месяц назад

So good, Matt!

@QuantenMagier 2 месяца назад

I always was a fan of the Icosahedron, but this video made me appreciate the Dodecahedron.

@mikeychrisanthus9948 2 месяца назад

The subtle joke for diagonals in space about 4 minutes in was really good. I imagine you were thinking, this is a bit silly, no one’s gonna even care. I care. That caught me off guard.

@eamonnsiocain6454 2 месяца назад

Excellent graphics!

@InhumanEntity 2 месяца назад

Rollie Williams would be proud of the video's style I reckon

@Howtheheckarehandleswit 2 месяца назад

There are, in fact, more than 5 regular polyhedra! jan Misali has a great video on this, titled "There are 48 regular polyhedra" if I recall correctly

@degv364 2 месяца назад

It hits better when you can visualize it in real life. Thanks Matt

@itsEnyo 2 месяца назад

man my workbook is getting full thank you for that note

@joelcooper6441 2 месяца назад

great vid, and looking forward to your book and, as a UK resident, can't wait for the 6th day of 20th month to get it

@unpythonic 2 месяца назад

This is one of the most awesome things I've seen. So much better than CGI

@nanamacapagal8342 2 месяца назад

Fun facts: - The two intersecting tetrahedra are the basis for the Skewb puzzle, which is actually an officially recognized event by the WCA. Only one of these tetrahedra is used for the core, however. - The figure in the thumbnail appears in WTMMP's post "STOP DOING MATH", which became even more popularized by Gianni Matragrano's voiceover.

@heugvlinder 2 месяца назад

What a lovely coincidence I'm building nested platonic figures in bamboo sticks (up to 3m) with my students at the moment and analyzing this video is their homework. Thanks, Matt.

@TheGeoffable 2 месяца назад

Brilliant example of fairly simple geometry being done really, really beautifully, love the UV :)

@volodyadykun6490 2 месяца назад

You are on fire, so many videos

@jasperjames123 2 месяца назад

8:34 "Write that down in your workbooks" 🤣

@jordank195 2 месяца назад

Excited for Alex’s cube animation

@radguitar1 2 месяца назад

I ❤ geometry. This video was so enjoyable.

@the3nder1 2 месяца назад

Imma need that track. 🎶"I couldnt be bothered."🎶

@sachiel197 2 месяца назад

*Diagonals in Spa-*

@Fasteroid 2 месяца назад

This was deeply satisfying to learn. I want to build one for myself now!

@Hamuel 2 месяца назад

The long awaited cube asset video!!

@Wielorybkek 2 месяца назад

loved it! dodecahedrons are awesome

@Epinardscaramel 2 месяца назад

I love that video of you with Adam Savage!! (the old one 😃)

@ahsanuddin89 2 месяца назад

Did not disappoint with the Steve Mould banter.

@neiliusflavius 2 месяца назад

I like how the cable ties make dotted lines under the black light.

@NickCombs 2 месяца назад

Adding new shapes to the friends list!

@Zosso-1618 2 месяца назад

The cube inside the dodecahedron is actually how Euclid himself constructed the dodecahedron! Check out Book 13 of his Elements, it’s proposition 17!

@jochi8874 25 дней назад

Id love the multicoloured luminous compound polyhedron as a pendant

@simonpenny2564 28 дней назад

at the boring end of the range, there are two intersecting tetrahedra in a cube - the edges of the tets being the diagonals of the cube faces. The centers of thee faces of an octahedron are the corners of a nested cube - and vice versa.

@GlizzyTrefoil 2 месяца назад

A cube with roofs on the faces? So that the roof planes of one face continously match up with the roofplanes of the neighbour faces. Or the triangle part of one roof matches up with the trapezium part of another roof to make the pentagon without any kinks. LOVE IT!

@Loki- 2 месяца назад

This is one of those satisfying videos. 😌

@CaineDM1955 Месяц назад

Consider: "2 Intersecting Tetrahedrons" (also known as a "Stella Octangula") are enclosed by a cube, & since "5 Intersecting Cubes" are enclosed by a Dodecahedron, it means that "10 Intersecting Tetrahedrons" can also be called "5 Intersecting Stella Octangula".