The ALMOST Platonic Solids

[@TheWolfboy180]

I think my favorite Johnson solid has to be the Snub Disphenoid. The idea that a "digon" (line) has a use case at all as a polygon, despite being degenerate, is just so funny to me.

[@terdragontra8900]

yes! i get a weird sense of joy using degenerate cases in math, such as for example, 0! = 1actually being intuitive if you think about it, there really is exactly one way to arrange 0 items in a line on your desk after all.

[@Omicron23-sj4wu]

its also funny to say "Snub Disphenoid"

[@Buriaku]

Yeah! I once tried designing a Rubik's-cube-like twisty puzzle with the snub disphenoid. It bent my brain.

[@soleildj1572]

I like the snub disphenoid, partly because the name is silly and partly because Vsauce mentioned it, mostly because I think it's pretty.

[@marcomoreno6748]

​@@Buriaku"... you must realize the truth." "And what is that?" "It is not the snub disphenoid that bends, it is you."

[@craz2580]

Son: "dad, why is Daisy called like that?" Dad: "because you mother really loves daisys" Son: "i love you dad" Dad: "i love you too Great Rhombicosidodecahedeon III"

[@TheCreator-178]

Nah you should have named him "Disdyakis Triacontahedron"

[@taxing4490]

Dad, why is Daisy called like that? Because when she was young a daisy fell on her head. And how did you come up with my name? No further questions whilst I'm reading, brick.

[@MyMohanta]

Isn't the last johnson solid the shape of a diamond.

[@Johnny_Franco-12_Scratch]

@@taxing4490Oh no

[@theodriggers549]

@@TheCreator-178 Should have called it gyroelongated pentagonal birotunda

[@chaotickreg7024]

I can't describe my panic at the Dungeons & Dragons table looking at my dice and realizing that there were so few regular platonic solids. I bothered my DM about it for weeks. And then finally I saw in a video showed there are very many regular platonic solids as long as you don't care what space looks like, and that put my mind at ease. A good collection of *almost* regular objects is going to seriously put my mind at ease. I should make plush versions of these solids to throw around during other hair pulling math moments. Yeah this is really giving context to the wikipedia deep dive I tried to do. Lots of pretty pictures but they didn't make sense until you showed the animations.

[@TrueAnts1]

d10 and percentile dice are pentagonal trapezohedrons

[@estherstreet4582]

If you want more dice, the catalan solids all make nice fair dice. The disdyakis tricontrahedron makes a particularly great dice, with 120 sides you can replicate any "standard" single dice roll by just dividing the result, since 4,6,8,10,12,20 are all factors of 120.

[@emilyrln]

Plush solids would be so cute! Might want to use mid- to heavy-weight interfacing on the faces so they don't all turn into puffy balls when stuffed with polyfill… although that could be cute, too, especially if you marked the edges somehow, e.g. by sewing on some contrasting ribbon or cord (you could ignore this step or use different colors for the adjacent faces). Now I want to make some 😂 I sewed some plushie ice cream cones recently and have been itching to make more cute things.

[@Green24152]

can't wait for when we figure out a way to make dice in the shape of the star polyhedra

[@AkamiChannel]

I can describe your panic: trivial

[@HesterClapp]

I've watched this once, twice opposite, twice non-opposite and three times and I still don't really understand all of them

[@binauraltreatments6178]

Vastly Underrated Comment

[@Axcyantol]

understandable

[@lucapri]

"twice non-opposite"

[@LexiLex421]

What? It’s sight readable.

[@AsgharH238]

It's interesting how (1,2o,2no,3) is a recurring pattern among the Johnson solids

[@Harmonikdiskorde]

This was so chilling and exciting. And also as an origami person, I was basically thinking of how to construct each one!

[@NikiTricky2]

Omg platonic solids

[@Kona120]

Why did I read this in the “omg I love chipotle” voice??

[@timpunny]

​@@Kona120platonic is my liiiiiiife

[@vaclavtrpisovsky]

> platonic solids But wait! There's more!

[@Han-b5o3p]

Almost

[@JGM.86]

😑

[@DissonantSynth]

Spectacular video! I also enjoyed Jan Misali's video about "48 regular polyhedra" which talks about some of the ones you excluded at the beginning

[@jan_Eten]

same

[@KinuTheDragon]

I came here to mention that video, lol.

[@jan_Eten]

@@KinuTheDragon same

[@choco_jack7016]

same

[@malkistdev]

Same

[@terdragontra8900]

rhombic dodecahedron is my favorite among all these guys. i like how unfamiliar it looks even though it has cubic symmetry. and its 4d analogue, the 24 cell, is completely regular! i wish i could look at it, its beautiful

[@nnanob3694]

It's even better when you realize it can tile 3d space! That's something most Platonic solids can't even do

[@terdragontra8900]

@@nnanob3694 hey, this guy gets it! :)

[@brianfisher4858]

Thanks! Great video. Have you ever looked at the geometric net of these kinds of solid. I know the cube has 11 possible nets. I would like to see a video that dives into the possible nets of some of the other shapes as well.

[@Kuvina]

Thank you so much! I do have some degree of experience with the nets of the catalan and archimedean solids after making them all out of paper. Some of them I even modified to fit better on 1 piece of paper!

[@malkistdev]

I just started watching this channel and I love how you can visualize and explain all this information in a way that is easy to understand. Great video! 😁

[@johncenee]

pixel land guy

[@blumoogle2901]

The most important thing I noticed in this video is a new way to get to irrational numbers and ratios via geometry

[@someknave]

For dice, face transitivity is much more important than corner transitivity, so Catalan solids are much more useful.

[@funwithtommyandmore]

magic man*

[@ToadJimmy]

Beautiful very well done and well paced video! I love it and thanks!

[@Yvelluap]

never before have i ever thought "damn i wish i had a collection of archimedean solids in my house" and then i saw 1:11 and spontaneously melted

[@funwithtommyandmore]

I want one too but they cost like 80$ per shape lol

[@Yvelluap]

@@funwithtommyandmore they look like paper though, i'm sure an exacto knife and strong enough glue should be enough to recreate them

[@funwithtommyandmore]

@@Yvelluap looks like weeks of work I'm not willing to put into some shapes lol

[@Descenacre]

Incredible video, great work on it all! A lot of new names for solids I never knew before A giant grid of all of the solids as a flowchart of different operations to get to them would be a hella cool poster tbh

[@redpepper74]

Omg I would totally buy that

[@crazygamingoscar7325]

Someones gotta make that, that'd be so cool!

[@TaranVaranYT]

@@crazygamingoscar7325maybe i can

[@Pixelarity64]

15:21 It must be my birthday! Look at that beautiful little chartreuse gremlin spin! Oh, how my heart radiates with joy!

[@kayleighlehrman9566]

Platonic solids Familial solids Romantic solids

[@onlykflow]

the kepler-poinsot polyhedra are sexual solids

[@asafesouza2015]

Dude WTF 💀

[@asafesouza2015]

Okay then sorry

[@alexterra2626]

Sexual solids- **gets shot**

[@KaesoARhombil]

Alterous solids

[@MinhAIPet]

Ranking Archimedean Solids: 1.Snub Dodecahedron 2.Rhombicosidodecahedron 3.Icosidodecahedron 4.Great Rhombicosidodecahedron 5.Cuboctahedron 6.Truncated Dodecahedron 7.Truncated Cube 8.Rhombicuboctahedron 9.Snub Cube 10.Truncated Icosahedron 11.Truncated Tetrahedron 12.Great Rhombicuboctahedron 13.Truncated Octahedron

[@RonuPlays]

with the music buildup at the end i was hoping for a scrolling lineup of all of the polyhedra lol. amazing explanation and 3d work btw

[@Zekiraeth]

I don't know why, but polyhedra like these are inherently appealing to me. I just really love me some shapes.

[@valentine6162]

Me watching this at 2 am, half asleep: “I like your funny words magic person”

[@MinhAIPet]

J27 = Pseudo Cuboctahedron J37 = Pseudo Rhombicuboctahedron J34 = Pseudo Icosidodecahedron The 3 Pseudo Archimedean Solids (Name it Kuvina solids or Minh solids (my name))

[@erikhaag4250]

if you take the deltoidal hexecontahedron. and force the kite faces to be rhombi, you get a concave solid called the rhombic hexecontahedron, and it is my favorite polyhedron

[@LeoStaley]

You'll probably enjoy this puzzle by Oskar can Deventer. kzbin.info/www/bejne/Z4OoqYt7rdCCqMk. The peices are almost rhombuses

[@FranklinWilliamWelker]

There's a rhombic hexecontahedron? I thought it's always a dodecahedron or triacontahedron.

[@erikhaag4250]

@@FranklinWilliamWelker There is, It's also the logo for wolfram alpha. en.wikipedia.org/wiki/Rhombic_hexecontahedron

[@MichaelDolenzTheMathWizard]

What's a rhombic hexecontahedron?

[@erikhaag4250]

​ @MichaelDolenzTheMathWizard en.wikipedia.org/wiki/Rhombic_hexecontahedron

[@KakoriGames]

A few years ago I was very intrigued about a very similar thing, but with tetrominoes, aka tetris pieces. It's well know that there's only 5 ways to connect 4 squares on a plane, with 2 of them being chiral, hence the 7 tetris pieces we all know, but once you start to dig deeper you start to have so many questions. What about 5 squares? 6 squares? 7? What about other shapes, like triangles? Or maybe cubes in 3D, aka tetracubes? What if you keep only squares, but allow them to go in 3 dimensions (they are called Polyominoids)? Turns out there's lots of ways one could extend the idea of tetrominos, by either using different shapes, getting into higher dimensions or simply changing the rules of how shapes are allowed to connect.

[@Kuvina]

I've been interested in that also! Not counting reflections, there are 12 pentominoes, and it's a classic puzzle to arrange them into a rectangle. You can actually make 4 different types of rectangle, 3x20, 4x15, 5x12, and 6x10.

[@zactron1997]

This is an excellent followup for Jan Miseli's video on a similar topic! Thanks for making this!

[@chaotickreg7024]

I had a weird math panic attack when I learned there weren't more platonic solids and that Jan Miseli video really put my mind at ease, and then went even farther and blew my mind a few times. Great video. And his stuff on constructed languages has taught me so much about linguistics that just keeps coming up in my regular language study, it's awesome. Love that guy.

[@nullifier_]

🥜 : cube 🧠 : square prism 🌀 : triangular trapezohedron

[@funwithtommyandmore]

🤓: inverted truncated triangular trapezoidhedronakaliod

[@KaesoARhombil]

Supertriakis tetrahedron.

[@haipingcao2212_.]

pirax

[@0ans4ar-mu]

my favourite solid has always been the truncated octahedron because it evenly tiles space with itself, and it has the highest volume-to-surface-area ratio of any single shape that does so. its the best single space filling polyhedra! if you were to pack spheres as efficiently as possible in 3d space, and then inflate them evenly to fill in the gaps, you get the truncated octahedron

[@AlphaFX-kv4ud]

So basically it's a 3d version of the hexagon

[@Currywurst-zo8oo]

I dont think thats quiet true. The shape you get when inflating spheres is a rhombic dodecahedron. You can see this by looking at the number of faces. The truncated octahedron has 14 faces but a sphere only has 12 neighboring spheres.

[@0ans4ar-mu]

youe could well be right, im no polygon-zoologist @@Currywurst-zo8oo

[@SkyBlue2010-f5m]

3:18 is that my channel

[@JoseSanchezLopez-yf3lo]

this is by far the best video I've seen on the topic! it's incredibly well explained

[@BinglesP]

Bejeweled gems timestamps: 0:06 Amethyst Agate (Tetrahedron), Amber Citrine (Icosahedron), kinda Topaz Jade (Octahedron) 2:38 Ruby Garnet (Truncated Cube) 2:46 Quartz Pearl (Truncated Icosahedron/"Football" shape) 16:12 Emerald Peridot (Deltoidal Icositetrahedron) 20:11 kinda Sapphire Diamond (Halved Octahedron)

[@feelshowdy]

OMG thank you for this comment, I was wondering about this!

[@BinglesP]

@@feelshowdy It's not 100% accurate, because not all of the Bejeweled gems are platonic or almost platonic solids of course, but I wanted to include all of them in the comment since they're all so equal to each other.

[@orrinpants]

Why are you calling this ⚽ a football that's obviously a soccer ball there's a giant difference

[@dysphoricpeach]

this is fast becoming my favorite video on youtube. i'm so happy to see that there are other people out there who care this much about polyhedra. the disdyakis triacontahedron is also my favorite, it's like a highly composite solid! just as 120 is highly composite! this is closely followed by the rhombic dodecahedron (because it's like the hexagon of solids!) and then the rhombic triacontahedron. this video has taught me so much, like how snubs work, and the beautiful relationship between the archimedean and catalan solids. not to mention half triakis (i had always wondered how someone could think up something as complex as the pentagonal hexacontahedron.) and johnson solids! i hadn't even heard of them before this video! thanks for educating, entertaining, and inspiring me! i'm so glad i stumbled across this. 120/12, would recommend

[@Kuvina]

Thank you so much! This is one of the most in depth comments of praise I've received and it's very encouraging :)

[@samueldeandrade8535]

My Euler! This channel is a gem!!!

[@saddo.masochist]

Great now I need a hystericaly elaborate polyhedra family tree diagram >:(

[@stickfiftyfive]

Watching this for the 17th time. Thank you for getting this all this down into one video. I can tell you worked really hard to put all the faces together for this one. 🎉

[@moslem2461]

You should make a video about tilings and hyperbolic tilings.

[@MinhAIPet]

Ranking Platonic Solids: 1.Icosahedron 2.Octahedron 3.Cube 4.Tetrahedron 5.Dodecahedron

[@NickenChicken]

Now I wish I had hundreds of magnet shapes, so that I could make these in real life. They look so collectible.

[@blekitYT]

2:57 is it the reference to an classic game named "soccer (in American English, in British its football)"?

[@clarise-lyrasmith3]

I have been trying to find a good explanation of Johnson Solids for YEARS and this one finally satisfies me. Thank you :D

[@ramonhamm3885]

This is a most excellent video! As a 3d puzzle designer and laser polyhedra sculptor, this helps show the relations between the shapes. ⭐

[@Johnny_Franco-12_Scratch]

Truncated Icosahedrons = soccer ball pattern

[@JoeBrowning-n9k]

Yes! I was wondering when someone would notice! 😄

[@Johnny_Franco-12_Scratch]

@JoeBrowning-n9k yes, i did noticen

[@MinhAIPet]

Do we have Johnson duels?

[@許富盈-u2t]

I saw descriptions about these solids at high school, and couldn't grasp many concepts yet getting really intrigued. Your explanation was excellent. Thank you sooooo much!!

[@jkershenbaum]

Really fantastic video! You did a beautiful job with the visuals and in organizing the explanation. I have shown it to a wide range of viewers - from a 7 year old to a guy with a phd in math. Everyone loved it and had the same basic reaction - it was entrancing!

[@DissonantSynth]

The shapes are all so beautifully presented; could you please share the software you used? Or is it a code library, perhaps?

[@Kuvina]

I used blender! You can download all the STLs from wikimedia commons, and they're automatically public domain since they're simple geometry!

[@DissonantSynth]

@@Kuvina awesome; many thanks!

[@vaclavtrpisovsky]

​@@KuvinaI didn't know Wikimedia hosts 3D files. Thanks!

[@Drachenbauer]

The hebesphenorotunds (last one explained 27:03) looks really similar a gem-cut. Think about the side with the 3 pentagon down into the socket and the hexagon outside and visible.

[@colettekerr279]

Gonna be printing some of these. A+ infodump. Super well done

[@a-love-supreme]

i really liked all the solids constructed with lunes! my favourite has to be the bilunabirotunda, it's just so pretty

[@PMA_ReginaldBoscoG]

Us: How many 3-d solids you want? Kuvina Saydaki: yes

[@someasiandude4797]

Imagine having dice of every single one of these

[@ironicdivinemandatestan4262]

The Dice Lab is a company that makes some unusual ones. Their large set has a truncated tetrahedron, truncated octahedton, rhombic dodecahedron, deltoidal icosahedron, disdyakis dodecahedron, deltoidal hexecontahedron, and disdyakis triacontahedron.

[@1.4142]

I need a bucket of blocks with solids from each family to play with

[@MatthewConnellan-xc3oj]

Yes

[@ArmyFrog]

This video fulfilled a craving I’ve had for years. Thank you.

[@SunroseStudios]

these shapes are really cool, we enjoy how ridiculous the names get lol

[@leannviolet]

Seriously the best use of visual examples in explaining these, I am sure there will never be a better explanation as long as I live.

[@CathodeRayKobold]

I've been looking into these solids for years, but had no idea what the process of discovering them was. Half-truncation is one hell of a leap, especially for someone born a few thousand years too early for computers. It's amazing he found them all

[@beimanuel942]

I LOVE WATCHING EDUCATIONAL GEOMETRY VIDEOS MADE BY NON BINARY PEOPLE ‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️

[@LeoStaley]

What's your favorite Johnson solid? Mine is the gyrobifastigium, which also has the best name, which you didn't even mention! You just labeled it j26! I like it because it just feels so symmetrical, like it should almost count as an archimedean.

[@FranklinWilliamWelker]

What's the gyrobifastigium?

[@LeoStaley]

@@FranklinWilliamWelker youtube keeps deleting my comment. there's a Wikipedia article on it, and if you Google the term alongside the word dmccooey you'll find a site that let's you rotate it and look at different angles. There's I even a puzzle someone made on KZbin out of the shape.

[@oliverstack7055]

I watched this whole video and found at least five of my new favorite solids. They will never beat my favorite shape, the snub disphenoid! Also, please make a video on some of the near miss johnson solids.

[@michaellyga4726]

This KZbin video has earned a spot in my all-time top 100, and definitely on the upper end of that 100. I’ve been watching YT since 2007. You’re seriously underrated, so if it helps, you’ve earned a new subscriber.

[@inheritedwheel2900]

I'm thankful another person has commented on the incredible quality of this video. I agree!

[@LeoStaley]

I was so happy when you included those 4 honorary platonic solids!

[@nono-xm8yl]

Your color choices for each polyhedron are lovely. This whole video tickles my brain wonderfully. I want a bunch of foam Catalan solids to just turn over in my hands.

[@Kuvina]

Thank you! I put a lot of thought into the colors so I'm really happy that it goes appreciated!

[@anthonyalgodoo40411]

20:35 Johnson Solids J01 Square Pyramid J02 Pentagon Pyramid J03 Triangular Cupola J04 Square Cupola J05 Pentagonal Cupola J06 Pentagonal Rotunda J07 Elongated Tetrahedron J08 Elongated Square Pyramid J09 Elongated Pentagonal Pyramid J10 Gyroelongated Square Pyramid J11 Gyroelongated Pentagonal Pyramid J12 Triangular Bipyramid J13 Pentagonal Bipyramid J14 Elongated Triangular Bipyramid J15 Elongated Square Bipyramid J16 Elongated Pentagonal Bipyramid J17 Gyroelongated Square Bipyramid J18 Elongated Triangular Cupola J19 Elongated Square Cupola J20 Elongated Pentagonal Cupola J21 Elongated Pentagonal Rotunda J22 Gyroelongated Triangular Cupola J23 Gyroelongated Square Cupola J24 Gyroelongated Pentagonal Cupola J25 Gyroelongated Pentagonal Rotunda J26 Twisted Triangular Biprism J27 Twisted Triangular Bicupola J28 Twisted Square Bicupola J29 Square Bicupola J30 Twisted Pentagonal Bicupola J31 Pentagonal Bicupola J32 Pentagonal Cupola-Rotunda J33 Twisted Pentagonal Cupola-Rotunda J34 Twisted Pentagonal Birotunda J35 Elongated Triangular Bicupola J36 Twisted Elongated Triangular Bicupola J37 Pseudo Rhombicuboctahedron J38 Elongated Pentagonal Bicupola J39 Twisted Elongated Pentagonal Bicupola J40 Elongated Pentagonal Cupola-Rotunda J41 Twisted Elongated Pentagonal Cupola-Rotunda J42 Elongated Pentagonal Birotunda J43 Twisted Elongated Pentagonal Birotunda J44 Gyroelongated Triangular Bicupola # J45 Gyroelongated Square Bicupola # J46 Gyroelongated Pentagonal Bicupola # J47 Gyroelongated Pentagonal Cupola-Rotunda # J48 Gyroelongated Pentagonal Birotunda # J49 Square Pyramid on Triangular Prism J50 Two Square Pyramids on Triangular Prism J51 Three Square Pyramids on Triangular Prism J52 Square Pyramid on Pentagonal Prism J53 Two Square Pyramid on Pentagonal Prism J54 Square Pyramid on Hexagonal Prism J55 Two Opposite Square Pyramids on Hexagonal Prism J56 Two Non-Opposite Square Pyramids on Hexagonal Prism J57 Three Square Pyramids on Hexagonal Prism J58 Pentagonal Pyramid on Dodecahedron J59 Two Opposite Pentagon Pyramids on Dodecahedron J60 Two Non-Opposite Pentagon Pyramids on Dodecahedron J61 Three Pentagonal Pyramids on Dodecahedron J62 Two Cuts From an Icosahedron J63 Three Cuts From an Icosahedron J64 Three Cuts From an Icosahedron + Tetrahedron J65 Triangular Cupola on a Truncated Tetrahedron J66 Square Cupola on a Truncated Cube J67 Two Square Cupolas on a Truncated Cube J68 Pentagonal Cupola on a Truncated Dodecahedron J69 Two Pentagonal Cupolas on Truncated Dodecahedron 1 J70 Two Pentagonal Cupolas on Truncated Dodecahedron 2 J71 Three Pentagonal Cupolas on a Truncated Dodecahedron J72 Twisted Rhombicosidodecahedron J73 Double Opposite Twisted Rhombicosidodecahedron J74 Double Non-Opposite Twisted Rhombicosidodecahedron J75 Triple Twisted Rhombicosidodecahedron J76 Cut Rhombicosidodecahedron J77 Opposite Cut and Twist Rhombicosidodecahedron J78 Non-Opposite Cut and Twist Rhombicosidodecahedron J79 Cut and Double Twist Rhombicosidodecahedron J80 Opposite Double Cut Rhombicosidodecahedron J81 Non-Opposite Double Cut Rhombicosidodecahedron J82 Double Cut and Twist Rhombicosidodecahedron J83 Triple Cut Rhombicosidodecahedron J84 Snub Disphenoid J85 Snub Square Antiprism J86 Dilunic Octahedron J87 Dilunic Octaherdon + Square Pyramid J88 Dilunic Icosahedron J89 Trilunic Icosahedron J90 Gyroelongated Elongated Octahedron J91 Dilunic Rotunda J92 Hexagonal Dilunic Rotunda The End.

[@TheMDCXVII]

pentagonal hexecontahedron is clearly my favorite with it's "petal" sides if you consider 5 faces connected on their smallest angle, or heart shaped sides, if you only consider 2 faces

[@robkb4559]

Great video - I've been fascinated by polyhedra for decades and I learned some new things here. Well done!

[@phobosdiscord5183]

You deserve way more than 4k subs, this a brilliant video

[@-NGC-6302-]

I was expecting this to be like a reduced version of Jan Misali's video about the 48 regular polyhedra... what a fantastic surprise! I love geometry, those were some great explanations.

[@davecgriffith]

Had to pause to comment - this video is excellent. Great job. Interesting topic, good visuals, good narration. Kudos!

[@muuubiee]

This channel is going onto the list. Hopefully once this nightmare of a degree (math) is done I'll have time to get through these interesting videos/topics.

[@epikoof]

i'm honestly surprised that you've explained it this well, i was able to keep up pretty much the whole time,, i was so shocked that i could understand what was happening i want to commend you for the use of color coding for things like rotundas and cupolas, you've done an amazing job at making this more digestible and it was very helpful excellent job on the video, kuvina

[@Random_Nobody_Official]

I want a toy set that's just all of these solids, not sure what i'd do with them, but it seems cool...

[@robo3007]

There is another category of almost platonic solids where you only use property 1 and 2 and don't care about the verticies being identical. These are the triangular bipyramid, pentagonal bipyramid, snub disphenoid, triaugmented triangular prism and gyroelongated square bipyramid, otherwise known as the irregular deltahedra.

[@M.Makart]

Wow, haven't seen so clean, concentrated and convenient explanation, without unnecessary effects it's even easier to understand. Your format is my favorite among others since I went in for geometry 11 years ago. My suggestion for next topic is "3D Honeycombs" because it's logical continuation of solids. There are "regular" ones which consist of the same solids you were talking about in this video. The particularly brilliant thing is there were found some irregular (!) 3D honeycombs. Most of them are of similar polyhedra, both convex and not. The only irregularity in them were the colors which cube faces had or something like this. But maybe there are some of them I missed which look like 3D version of Penrose tiling. Edit: Pentakis Dodecahedron is my favourite solid (the second one is Icosahedron) because it's one of the roundest solids which consists of equal polygons.

[@bandana_girl6507]

I am a particular fan of the disdyakis triacontahedron because it is the largest roughly spherical face-transitive polyhedron, so it's the largest fair die that can be made (ignoring bipyramids and trapezohedrons)

[@JoeBrowning-n9k]

2:04 Hmmm... Corner cutting, are you a cuber?

[@Kuvina]

Yes I'm a big fan of anything involving colorful shapes

[@JoeBrowning-n9k]

@@Kuvina no, a cuber is someone who is interested in Rubik's Cubes.

[@Kuvina]

Ik lol I have a huge collection, I was just saying that's why I'm probably so drawn to them :)

[@JoeBrowning-n9k]

@@Kuvina oh.

[@malakirizvanovic4250]

I am

[@pinethetree]

Let's face it most underrated youtuber I have ever come across (is you)! Well done and Thank You, you are a wonderful edgeucator c: who always gets even very complicated points across, not to mention the volume of information in each video is enormous!

[@clockworkkirlia7475]

I'm trying to get a pun in here but your comment fills so much of the available space that I'm pretty sure it's a tileable solid!

[@lord0fthecubes]

I hate to be that guy but 15 seconds in, the icosahedron is labeled as a dodecahedron. That's the only thing I could think of that was wrong with this video. Amazing work!

[@funwithtommyandmore]

Lol there is 2 Dodecs

[@Gamr-bc6kp]

ENBY DETECTED!! LOVE, AFFECTION, AND SUPPORT MODE ACTIVATED!!

[@jonahwolfe3396]

Thank you for such an interesting video. A lot of these I was hearing about for the first time and I found great joy in hearing you pronounce the name, getting surprised that this one is longer than the last one, and then laughing as I struggled to pronounce the name myself. My favorite was either the “Snub Dodecahedron” or the “Pentagonal Hexacontahedron”. The Snub Dodecahedron looks so satisfying having a thick border of triangles around the pentagon, but there was something about that Pentagonal Hexacontahedron that I found really pretty. I think it’s because of the rotational symmetry. Again, thank you for taking the time to make such interesting and engaging videos. I look forward to watching another one.

[@TheWanderingCell]

mine too!

[@rosiefay7283]

5:18 Those corners are absolutely all of the same type. You imply that corners that can be rotated onto each other have the same type. The same goes for reflections. For me, appeal to your alternative definition in terms of vertex transitivity is valid but isn't necessary.

[@Kuvina]

To be honest, I was expecting pseudo rhombicuboctahedron fans who would potentially get mad about how it's excluded from the archimedean solids (honestly if it were up to me, I might define things differently), so I introduced the idea of vertex transitivity earlier so that there would be a basis for it being part of the definition, and so it wouldn't be mentioned just to exclude the pseudo rhombicuboctahedron.

[@MinhAIPet]

Ranking Catalan Solids: 1.Rhombic Triacontahedron 2.Disdyakis Triacontahedron 3.Triakis Icosahedron 4.Pentakis Dodecahedron 5.Triakis Octahedron 6.Pentagonal Hexecontahedron 7.Rhombic Dodecahedron 8.Deltoidal Hexecontahedron 9.Disdyakis Dodecahedron 10.Triakis Tetrahedron 11.Deltoidal Icositetrahedron 12.Pentagonal Icositetrahedron 13.Tetrakis Cube

[@TheJelocake]

Came for the 3d shapes Stayed for the enby explaining the 3d shapes

[@ezdispenser]

i like the cupolas also i admire how you were able to say so many syllables so confidently lol- it probably took a few takes

[@zackf13]

First time seeing any video of yours, already my favorite enby math teacher

[@furbyfubar]

8:41 "and anything more than 360° requires hyperbolic geometry" This made me pause the video and go "No, you could just fold some of the folds inwards, so this proof can't hold unless there are more than those 2 criterias for what is an Archimedean solid!" I just checked wikipedia. Both Platonic and Archimedean solids *also* have the criteria that they have to be convex. That said, I have no idea if it would be possible to generate other Archimedean solids if concave ones were also allowed. The type of solid I'm thinking of isn't the en.wikipedia.org/wiki/Kepler%E2%80%93Poinsot_polyhedron solids, as they all have intersecting planes. What I'm thinking of would be a non-convex solid made up by only regular polygon and every corner is identical, yet doesn't have any intersecting sides. But it's very possible the reason the type of solid I'm thinking of simply can't exist, so that's why I can't find them on wikipedia. I invite you or anyone else reading this to get nerd sniped by this, so that *I* don't have to go down the rabbit hole of disproving/finding them. Or if anyone knows that they exist and have a name, then I'd really appreciate a reply with their name.

[@thepulsarx5896]

11:50 i like the pacman reference

[@furbyfubar]

I still think the webcomic Oglaf gave the best definition for a Platonic solid: "Any shape that doesn't want to fuck you" (If you couldn't tell from that quote, Oglaf is quite NSFW.)

[@Pablo360able]

Even as someone who knew where most of this was going in the first half, I didn't realize why you were delaying explaining the relationship between the cube, octahedron, and cuboctahedron until you started talking about duals.

[@PrairieKass]

this video was really good I enjoyed it a lot. good explanation of each in a way that was easy for me to understand and cool visuals. you earned yourself a sub from this. I really loved this video

[@soleildj1572]

I love this video! I'm glad that I found your videos. I have a love for mathematics and geometry, and it's cool someone made a video about platonic-y solids! I liked the video "there are 48 regular polyhedra" by jan Misali and this is the type of stuff I like. I think you would like that video, too.

[@brawlholic9960]

What about Chamfered Platonic solids(Goldberg polyhedra)? For instance, with Chamfering (edge-truncation) you can make from a Cube a Chamfered cube, and if you continue it leads to a Rhombic Dodecahedron wich is a Catalan solid! So if you think about it, you can skip the Archimedean solids which by the way are really similar (Chamfered cube-truncated octahedron, Chamfered Dodecahedron-Truncated Icosahedron) but not the same, and go straight to their Duals(Catalan)! I know that they made by congruent flattened hexagons/polygons instead of regular one but, aren't these unique solids worth mentioning or not?

[@noone-ld7pt]

sensational video! Loved the term honorary platonic solids, definitely stealing that one! My personal favourite is the rhombic dodecahedron! :)

[@whistling.citrus]

The blender is incredible! I love the little introductory twirl tytytytyty

[@MrBrain4]

This is an incredible video. Fantastic job, and thank you!

[@PretzelBS]

I have no idea how you make everything feel so concise and ordered. If I wanted to research this it would be so messy

[@louiesumrall358]

I LOVED this video!! I am a huge geometry nerd and learning about polyhedral families and the construction methods to generate new ones makes them all feel so intertwined and uniform. If I may request, please do a video on higher dimensional projections into the third dimension like fun cross sections of polytopes through various polyhedra. TYSM

[@silas6446]

this channel is so underrated love your videos!!!!

[@lexinwonderland5741]

Amazing video!!! Very in depth and yet easy to follow, I really enjoyed some of the smaller details like sphericity!! i look forward to your future uploads!!! -from another friend of Blahaj ;)

[@cheshire1]

My favourite catalan solid is the pentagonal hexacontahedron. I find it very pretty how the flower patterns with 5 petals interlock to make chiral corners at the boundary.

[@aidanmaniaMusic]

These are incredibly interesting, like platonic solids but stranger and there are way more. Love it!

[@atrus3823]

Just discovered your channel and am loving it. You are covering all my favourite topics. I personally find the Catalan solids more beautiful than the Archimedean ones.