Making efficient Platonic and Archimedean shapes in a kaleidoscope

Sign up on Patreon for the SUM xmas card! / standupmaths If you want the physical card you need to be greater than or equal to "Statistically Significant".
Physical card deadline: end of 06 December 2022
Digital card deadline: end of 15 December 2022
(In both cases I'll try to accommodate sign-ups after that but no promises).
This is why the christmas tree on the card is so low resolution: • Can the Same Net Fold ...
Here is the "Deltoidal kaleidoscopes" paper by Josep Rey Nadal and Manuel Udina Abelló.
archive.bridgesmathart.org/20...
Museu de Matemàtiques de Catalunya aka "Museum of Mathematics of Catalonia" mmaca.cat/en/
This is the art show listing from the 2022 Bridges conference in Helsinki. gallery.bridgesmathart.org/exh...
For both kaleidoscopes make two mirror images of each shape.
Deltoidal Hexacontahedron Kaleidoscope Faces: www.dropbox.com/s/9tltpyo4v6k...
Deltoidal Icositetrahedron Kaleidoscope Faces: www.dropbox.com/s/jb356rspfn5...
Here is the second channel video from 2017: "How to flat-pack a cube" • How to flat-pack a cube
Huge thanks to my Patreon supporters who funded so many sheets of mirror acrylic. I actually have a bunch left over. Support me and tell me what I should do with the rest of the mirrors. / standupmaths
CORRECTIONS
- None yet, let me know if you spot anything! My bad taping skills do not count as a mistake.
Filming and editing by Alex Genn-Bash
Shape calculations by Sam Hartburn
Written and performed by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...

[@estherstreet4582]

Imagine this hanging from the ceiling with the mirror acting like a "lampshade" and a bright neon tube light forming the shape, it would be such a cool light

[@hughcaldwell1034]

Absolutely going to try making something like this for my bedroom. My partner is bed-bound and we're both big maths nerds. Something like this would be a really awesome addition to the room, I think.

[@joemyers5302]

Could it be done if you make the walls out of mirrors?

[@gabor6259]

@@hughcaldwell1034 "We're both big math nerds." Ah, the perfect relationship.

[@airplanes_aren.t_real]

@@hughcaldwell1034 good luck, hope you have fun

[@MrPeetersmark]

You can use one way mirror. It reflects but it’s see through.

[@Ryan-in3ot]

i can't believe matt's room isn't lagging with all of that real time recursive rendering

[@00Krohnos]

His room is actually a fractal, which GPUs are extremely at fast at rendering - even in 3D!

[@stickmcskunky4345]

​@@00Krohnos.. when you say something potentially profoundly true in the guise of a bit

[@stickmcskunky4345]

There's mad lag, the brain just edits it out

[@robertthompson3447]

Matt: This is like a kaleidoscope but much more precise. Also Matt: I cut this myself with a jigsaw.

[@airplanes_aren.t_real]

Precision may need sacrifice

[@Jason-sq2up]

I thought he was saying kaleidoscopes are more precise

[@strehlow]

Measure with a micrometer. Mark with chalk. Cut with an axe.

[@NicolaiParsons]

It's a Parker kaleidoscope!

[@pyglik2296]

Actually he says "[...] much more precise, give or take.", so... he's not actually saying that it is more precise...

[@AlRoderick]

This reminds me of an idea I had for an artificial Christmas tree that's just a quarter of a tree, the idea being that you stick it in a corner between two mirrors so it looks like a whole tree but using a quarter of the floor space, materials and lights. I guess you'd call it a symetree?

[@chaos.corner]

This would be great. If you could make a tree that folded up if you pushed the mirrors together, that would be even better.

[@kyokoyumi]

@@chaos.corner Like a pop-up book

[@chaos.corner]

@@kyokoyumi I'd thought maybe that for different holidays but you'd need multiple layers of mirrors I'd think. Though there might be a way. But yes.

[@bathbomber]

You should patent and sell this idea!

[@MrMartinSchou]

And you can have lots of fun by having people try to dance around it.

[@JohnHollowell]

I think the main issue with your mirrors is that they are rear-surface mirrors so there is a acrylic-width gap in your edges which adds an offset to all the other reflections. A first-surface mirror would work a lot better I would think.

[@XMarkxyz]

How cool it would be with some aluminized material

[@rhamph]

@@XMarkxyz The extra reflectivity of silver would be dramatically better here due to the repeated reflections. Finding a suitable material at a reasonable price is the real challenge though.

[@bentfishbowl3945]

Or maybe just miter the edges with a file?

[@RonParker]

@@rhamph It used to be fairly easy to get glass first-surface mirrors from discarded microfiche readers and laser printers, but it's gotten harder to find suitable donors. You can also make your own mirrors with suitable chemicals. If you live in the US you can get a kit from Angel Gilding. (I work with leaded glass, so I've had their site bookmarked for years, but I've yet to actually buy one of their kits.)

[@CheaterCodes]

I think the best results would be achieved with a solid-glass pyramid with reflective coating on the outside. On the inside you would then have seamless first surface mirrors, but they are still protected by the glass

[@stevemonkey6666]

Matt's joy at this is palpable

[@quamrana]

Yes, I loved the 'Happy Matt' face!

[@vigilantcosmicpenguin8721]

And contagious.

[@jessicadaugherty9011]

This is the best!

[@alexandermcclureidrinkoliv3663]

*P*otent, *P*ungent, *P*alpable joy at the sheer mathematics. (pretend those P's are bold instead of surrounded)

[@idontwantahandlethough]

I love that the premise assumes, without question, that one absolutely NEEEEEEDS to carry their cubeyboi with them everywhere they go.

[@totoshampoin]

... you don't?

[@toxicara]

Matt should have called this "how to please mathematicians with shiny things"

[@angeldude101]

Only mathematicians? What kind of monsters are these "non-mathematicians" who _don't_ like shiny things?

[@jinclay4354]

@@angeldude101 Well, non-mathematicians might look at this and say "Ooo, pretty!", but only mathematicians will, after saying that, ask "How does it work?".

[@miorioff]

Every time Matt is saying something like "it's not perfect... but it's not bad... it's working....?" I'm like... it's Parker Square again isn't it? 🤣

[@ericgoldman7533]

Damn skippy! Matt is, after all, the patron saint of "giving it a go"

[@NanoMan737400]

Parker Cube this time, he's now growing in power!

[@toxicara]

the parkaleidescope, YES!

[@afrophoenix3111]

Parker Symmetry

[@Phriedah]

as they say, perfect is the enemy of progress. I love his 90% executions. Feels very real.

[@thealmightyduck335]

Seeing Matt get so incredibly giddy over shapes and reflections will always make me smile :)

[@bencheevers6693]

I have to admit after Matt said "you're just going to have to trust me" I figured he already knew that it wouldn't really turn out on video so he was bracing us for that not to expect much and that just floored me at the end how well it worked, really quite a good trick Matt

[@tomadil331]

As someone from a country as tiny as Catalunya I can't even begin to express the shock of watching yet another english video, seeing it mention a study from catalan mathematicians and then transition into a museum in a town minutes away from yours. It's like if your parents were to suddenly appear in the video.

[@CarMedicine]

Small correction: Catalunya (or "Catalonia" as the English say) isn't a country, it's part of Spain, but yeah it's very cool to have some English video mention where we live. (i also live in Catalunya)

[@EmyrDerfel]

@@CarMedicine You're expressing an opinion as fact. You and Tom evidently don't agree.

[@CarMedicine]

@@EmyrDerfel wut? it isn't an opinion. If it was, then saying "Brazil is a region of Japan." would also be an opinion. It isn't, it's just wrong.

[@tomadil331]

@@CarMedicine I particularly chose the word "country" because it's certainly not self-governed, hence it's not a "state", but I recognise its diffenenciated language and culture as characteristics for a "nation". It's like the USA, but instead of being a huge country divided into smaller states it's a big state containing some countries (like Euskadi, Galícia or the País Valencià), which happens all over Europe because the cultures spread more slowly than in America. Anyway, it depends a lot on what meaning you attribute to the word "country"😄

[@CarMedicine]

@@tomadil331 buddy, the term "comunidad/tat autó/ònoma" (autonomous community) exists for a reason.

[@dylanlasky2389]

That glowstick part was the clearest and coolest by far

[@johnchessant3012]

8:34 Fun fact: The entrance to MoMath is a glass cube where a regular hexagonal slice dividing the cube exactly in half is drawn in red.

[@SotS1689]

Who knew being a mathematician would also require pro status at arts and crafts? As always, very well done.

[@sachiperez]

Such a cool feeling when the brain forgets about the mirrors and just sees the object!

[@Toobula]

I knew a guy years ago who built these, but much larger so that you could stick your head down in there. He also put lights along the edges. The thing he did that Matt could have done here, is put a final rectangular mirror in the bottom. Then when you look in, you will not just see an icosahedron made out of wooden desk, but one with your face looking out of all the faces. It's amazing.

[@FishSticker]

THE ENDING WAS PERFECT

[@Dreju78]

Is this a ploy to make me watch to the very end?!😁

[@FishSticker]

@@Dreju78 it's a Matt Parker video, you should always watch to the very end

[@derekhasabrain]

Matt I am so grateful you have a KZbin channel. I remember my young self in middle school watching numberphile videos because I didn’t have many friends but I was passionate about math and it made me feel better seeing that other people were passionate about math as well. Here I am, about 10 years later, still watching my parasocial buddy Matt Parker Parkering his way through the world like me. Thank you for doing this

[@JalebJay]

The ending got me in awe. One of the coolest ideas I've seen.

[@pseudo_goose]

This makes me want to build a raytracer to emulate these kaleidoscopes! I think that would be a really cool way to experience this without having to build it.

[@incription]

Hey Matt, you should experiment with acrylic one way mirrors. If you cover a cube in this surface, the internal rays will bounce around the interior, creating the effect of an "infinite world" within the cube, like a wormhole.. You can exaggerate this effect with LED strips along the sides. Look up "LED Hypercube"

[@freescape08]

I like where you’re going with this, but instead of a regular hyper cube, what about a condensed hyper cube? Do what Matt did, but with clear acrylic on the outside ‘surface’ of the shape, to reflect another shape off of each reflected surface that’s visible on the far side of the main shape.

[@99parkerj]

Matt has done something like this before (with Adam Savage from Mythbusters): kzbin.info/www/bejne/bGbVkGSKr6-Ll7M

[@incription]

@@99parkerj DO IT AGAIN!

[@TheLostSorcerer]

I believe he has already done that with Adam Savage. kzbin.info/www/bejne/bGbVkGSKr6-Ll7M

[@RomanQrr]

If I remember correctly Matt and Adam Savage of Mythbusters fame already did make one of the "infinite" shapes.

[@nnanob3694]

It's really cool to see the shape and its dual in the same kaleidoscopic mirror! (Also: rhombic dodecahedron is the bestahedron)

[@Macieks300]

5:03 wouldn't be a Matt Parker video without the classic "just give it a go"😆

[@lrwerewolf]

Love that he immediately went to the bestagon. Also, love seeing him use half the dual of a cube to convert a single plane into a full cube.

[@rohitraghunathan]

"Like a kaleidoscope, but much more precise... Give or take" - Matt Parker, Dec 2022

[@torridice]

The level of joy displayed in this video is infectious. ❤️

[@JHaven-lg7lj]

When you dropped the glow stick in and just looked at it without saying anything I thought “He’s SO happy right now” which you immediately confirmed. Thank you, awesome video

[@AlexanderTBratrich]

Matt keeps confirming to me that Math(s)-people really like to play with things a lot. My old math teacher always did that (and I mean, it makes geometry even more fun than it already is!)

[@ronm3245]

I'm an old math teacher and I approve this message.

[@danielcarter6178]

This whole deal with constructing polytopes from kaleidoscopes is basically what Coxeter-Dynkin diagrams are. You will surely run across these diagrams if you look at Wikipedia pages on polytopes; they have nodes and edges and sometimes some numbers. Each node represents a mirror, and edges represent angles between mirrors. An unlabeled edge means to attach them at a 60 degree angle, an edge labeled "4" means a 45 degree angle, and "5" means a 36 degree angle. This is extended by putting circles around some of the nodes. This notation basically describes putting different things into the kaleidoscope to get different polytopes out. In the case of polyhedra, there are 3 nodes, and at least one node must be circled (otherwise you get a single point), so you get 2^3 - 1 = 7 polyhedra from any kaleidoscope. The keyword to look up here is "Wythoff construction." In the case of Matt's cube kaleidoscope, the 7 polyhedra you get are the cube, truncated cube, octahedron, truncated octahedron, cuboctahedron, truncated cuboctahedron, and rhombicuboctahedron. There are some extensions that decorate the nodes in other ways that can get you the rhombic dodecahedron and other shapes.

[@killerbee.13]

This is honestly a great demonstration of the idea of a dual shape, makes it a lot clearer than a lot of other things I've seen on the same subject.

[@omaanshkaushal3522]

If you could basically see it all at once, inside the kaleidoscope, it would be so much more dope than it is right now. Matt knows how to get his viewers to love Math

[@airplanes_aren.t_real]

Sounds like a map in a vr world

[@widicamdotnet]

They would've just needed to film it up-close with an extreme wide-angle lens (fisheye or so) to get the entire shape into view - closer to what you'd see if you held it up to your face.

[@mczs]

Matt that last experiment is utterly amazing! Thank you for showing us this!!

[@W9e0e2e3e4pizza]

The glow in the dark shapes are absolutely incredible! I feel like these could be made into some sort of decorations for Halloween or something....

[@ARKGAMING]

16:12 Matt's face here show how much fun he's having and it's amazing

[@NevinBR]

If you set the angle on your saw to half the angle between adjacent faces (this might be different for each pair of faces), then the seams where the mirrors meet will line up flush. You could even glue them on those edges if you’re careful.

[@donnerflieger3770]

I really like Matt discovering cubic symmetries. Really important in crystallography. I like how he made the minimal possible cell of F 4/m -3 2/m

[@IonicFox2nd]

Something about this topic seemed familiar, then I remembered that Matt was in an episode of Adam Savage's Tested where they built a similar object with light strips. Such a cool idea for a project. Makes we want to do one myself.

[@SpeckyYT]

I entered the premiere and it was literally at 5 seconds left

[@krissp8712]

I did wonder if it was a premiere, on mobile I had to bring up the pause overlay to confirm lol

[@asheep7797]

i came 9 minutes late

[@lichtenshtein345]

Bro wtf same exactly 5 seconds

[@jqsm1neS]

Lmao genuinely same

[@veggiet2009]

I really dislike premieres for this reason, as I never seem to join at the right time, I have to rewind for a weird amount of time, and then fast forward through the countdown... I would just rather stop and wait for the premier to be over

[@lewismassie]

Might be interesting to set some of these up in Blender, should be pretty easy plus the fact that the mirrors can let you see through them from the back like you were trying with the two-way mirrors. I was trying to make a true portal effect and stumbled across this exact thing by accident

[@LeavingGoose046]

L to whatever gpu tries this

[@lewismassie]

@@LeavingGoose046 I mean I was using a 960M (yes really) and it was okay so long as I hard capped the light bounces

[@kranziodelfantastico7433]

“I will admit it’s not perfect; it’s not bad. Has a few flaws.” -The Parker Credo

[@twertygo]

How have we deserved so many videos in such a short time ❤️

[@BeheadedKamikaze]

I am not yet convinced we deserve it. But I needed it ❤

[@mal2ksc]

You can get cleaner edges on acrylic by scratching a line into the surface (a ruler and X-Acto knife will be fine), and then breaking it.

[@vigilantcosmicpenguin8721]

I've never considered what a maths rave would be like but now I feel like that has to be a thing.

[@mctuble]

I have to tell you I love your child like curiosity and your ability and the means to follow through on taking these experiments to the next level. Keep up the great work! Look forward to every one of your videos

[@vitor-muzulon]

I just wanna point out to Matt that here in London, in the Grosvenor Square, there is an infinite mirror Rhombic Dodecahedron sculpture, like the one you made with Adam Savage

[@airplanes_aren.t_real]

Just saw it, it's beautiful

[@SineEyed]

There's a company that makes a deltoidal hexacontahedron infinity mirror sculpture which has high density rgb led strips lining all the interior edges. I think its about 1.5m diameter. This thing turned on might be the coolest thing you've ever seen..

[@airplanes_aren.t_real]

@@SineEyed what's the company

[@GuybrushThreepwoodNZ]

Superb maths and art mashup Matt! Thanks for the inspirational content.

[@jakobchang9781]

It's funny how the platonic solids are just being good friends while the archimedean ones are trying to screw you.

[@williamberman5978]

Nobody tell this guy about the Johnson solids

[@hashtagPoundsign]

What I love most about your project videos is that you make them very accessible, so that just about anyone can give it a go. On another note, you could make it as an infinity mirror with an led strip as the portion of the cube.

[@petrsokol588]

I mean it's really important that you just show us that this concept exists! That's a totally valid contribution. I'd have never known this existed, yet it is so cool!!!!

[@BeheadedKamikaze]

That was exceptionally cool Matt! Well done ❤

[@andersgleich4717]

WOW!... just on a trip following the idea of building trippy visualizations also in kaleidocope ways... it really made me happy when u replaced the mirrors with real ones... and it made me party hard when you took the glowlights. just what i hoped to see.. thx for making the builds and sharing the templates

[@randy7894]

A spectacular finale Matt!

[@ultimate0levels]

7:50 if each line is 1/8th of the circumference of a face, 24 lines make the entire cube, not 48.

[@thomilo44]

seconded

[@airplanes_aren.t_real]

So each line is ¼?

[@theofficialczex1708]

@@airplanes_aren.t_real Each line is 1/8th of a face, but the faces have coincident edges.

[@jonprudhomme7694]

Love the genuine enthusiasm 😍

[@jannegrey593]

Kaleidoscopes always fascinated me as a kid. I'm looking forward to this video. I'm sure I will enjoy it.

[@kayleighlehrman9566]

"Much more precise, give or take" What a phrase, Matt lol

[@RoyEltham]

You looked so pleased! It definitely is pleasing. The end bit with the glow sticks was deluxe!

[@OliveHavre]

Incredible ending

[@lunarmare0]

Hi Matt. Just wanted to let you know I listen to your videos, whilst for entertainment, but also sometimes as background noise whilst working on university studies. Your voice is really soothing. Thanks

[@gunagunter7367]

Really great ideas. Ive been playing with the platonic solids with wires and strings. this just makes it all easier on reflection

[@Spartacus005]

Hi Alex! Unsung hero of this channel

[@ColemanMulkerin]

This makes me unusually happy to see. I would like more videos on these constructions.

[@belgaer4943]

The visuals at the end are so otherworldly and stunning

[@paulzagieboylo7315]

I'm amazed at how well this works. Although everything that Matt describes as a "snub cube" is actually a cuboctahedron. You can get a snub cube this way but it's more complicated, you need one of the funny-shaped wooden inserts.

[@sannekimenai639]

I felt that ultimate joy at the glowsticks even through the screen!

[@Xxyter2]

3 videos in 2 weeks? You're too good to us, Matt.

[@davidg5898]

The 2-way mirror part at the end reminds me of an art installation, "N-Light Membrane" by design collective Numen/For Use. Except instead of manipulating symmetries, it would deform some of the sides with air pressure (making them convex or concave) to turn an infinite cubical lattice into varying degrees of infinite curved lattices.

[@kaninom_KAS]

This is actually amazing

[@guillermonassercibils6538]

THAT IS AWESOME! Also i just love your signature music

[@ponyote]

DJ Matt, dropping some knowledge and sick beats.

[@quirkbird1713]

This pure joy of an adult playing with kid's stuff deeply resonates with me. Kid's stuff, thats actually pretty complex and fascinating on second look.

[@crazygamer56]

Vibing to the music and looking forward to more Christmas tree lights this year!

[@nobodi6448]

i love this! so beautiful 🤩

[@CyrusMackie]

Absolutely beautiful

[@K-o-R]

0:36 "Through the magic of -buying- making two of them...!"

[@OrangeC7]

Imagine a version of this where you have those thin mirrors where you can shine light through to the other side, then you can build the one that does multiple shapes and just have displays directly behind the mirrors that shine the outline of the shape into the kaleidoscope

[@KiloOscarZulu]

I never thought maths rave would be a thing. But here it is!

[@arielioffe1810]

i’ve never taken that much time to appreciate the music on this channel

[@EPMTUNES]

Awesome showcase Matt!

[@ZeroOskul]

14:01 Hexacontahedron. A triacontahedron is a thirty-sided shape. A rhombic triacintahexahedron is a thirty-six-sided shape with each face being a rhombus and if you split each rhombus with a line of equal length to its sides you get an equilateral triangle-faced hexacontahedron which is a sixty-sided-shape. Hexacontahedron.

[@JustinDrentlaw]

That is super cool at the end! I wanna build one now!

[@ZeroOskul]

You are the living embodiment of rock 'n' roll, Maths Matt!

[@arielioffe1810]

whoever did this re-interpretation of the thene song did a very good job

[@laser8389]

I was not prepared for the lights-out version to be so cool!

[@chayam5904]

Loved the rave!!! I’m so happy to enjoy maths with other people who are excited as me about it 😅

[@tjgansenberg3121]

So glad I stayed until the end!

[@TotemStorms]

Very much enjoying that Matt's practise with Adam Savage was put to good use. When do we get to see the infinity mirror that Adam said he would be sending over?

[@derrickobara6806]

Really enjoying the musical crafts breakdown interludes of late.

[@Gbriel1234567890]

You made it look super cool too!

[@somedude5990]

This is amazing!

[@Mecharnie_Dobbs]

To more precisely position each mirror, you could use screws. Any object can be positioned in 3D space via height, depth (away), transverse, yaw, pitch and roll. 6 adjustable screws for each of the 3 or 4 mirrors. 3 of the directions for each mirror involve varying the distance between 2 objects (each) , whereas the other 3 involve varying the rotational alignment between two objects (each) using precise gears like indirectly moving the hour-hand of a clock, by directly moving the second hand.

[@Daltem]

Truly excellent

[@etepeteseat7424]

That final mirror at the end there is incredibly cool.

[@TheMCEnthusiastPlays]

this was just awesome

[@d3j4v00]

The outro music finally got the glow stick light show it's always wanted!

[@bloodypommelstudios7144]

The ending was really awesome.

[@curiositeperpetuelle8610]

That IS sooo beautiful, even your joy is lovely ^^

[@Cubium]

Omg Matt you are brilliant

[@JeroenBaxexm]

another must watch is the collab with adam savage. That was a great vid as well!