The ALMOST Platonic Solids 

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.

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"

Platonic solids Familial solids Romantic solids

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

Omg platonic solids

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.

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

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! 😁

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

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

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

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

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

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

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

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.

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

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

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.

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

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

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.

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)

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!

I loved this, especially the explanation on why there are only 13 Archimedian solids, great work!

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. 🎉

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!

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

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

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!!

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

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

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

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

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

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

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

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

Fascinating video, thanks for posting. Some years ago I assembled some of the Johnson Solids using Polydron (plastic panels that clip together)

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

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

Highly appreciate the compilation ❣️

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

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.

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

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.

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.

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 ;)

My Euler! This channel is a gem!!!

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

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

Your mathematical curiosity is beautiful and scary. Thank you.

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

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

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

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.

Solid work, my compliments!

You: "This is a truncated icosahedron." Football: Am I a joke to you ?

Excellent video! thank you so much

Wow thats one great video. To go through so many cases It must've taken a long time to make, good stuff

Loved the video!

I've been looking for a good video about this exact topic for ages. So glad there finally is one.

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

This RU-vid 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.

I absolutely love your videos

fantastic video!

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

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

I enjoy seeing these kind of videos about 3D solids, because it gives me a chance to try and build some of the shapes irl. I hadn't heard of the snub square antiprism before, that was my project to make during this video. I ended up making a poor paper one. I tried to make one with magnetic shapes, but the structure wasn't ever stable enough for me to properly connect it up. Still had a great time, tho! Solid video, thanks for introducing me to some new shapes!

I would love to see a video looking at the stellated versions of some of these and how the math works out for self-intersecting planes in these shapes

Awesome! Good work!

The Pseudo Rhombicuboctahedron is called "elongated square gyrobicupola". I love this video, could watch it over and over again. Thanks!

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

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.

4:37 You can also make a rhombicuboctahedron by expanding a cube, which is done by moving the faces away from the centre and then connecting them with rectangles on the edges and whichever polygon is needed on the corners. The same can be done but by rotating each face and connecting them with triangles instead of rectangles to make a snub cube

i gotta say i appreciate your choice of favorite catalan solid, but in my case i just really enjoy the rhombic triacontahedron. the chiral deltoidal ones are tough runners up though. for my favorite johnson solid i was pleasantly surprised to see the snub disphenoid be a thing (i completely forgot it existed), which i think is just more interesting to look at than any of the "take a prism and put a rotunda/cupola on its face, or don't". my favorite archimedean solid is probably the snub dodecahedron. as you might be able to tell, i like snubs :)

congrats on 6k subscribers

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.

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

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.

Very useful video, thank you.

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

I will now use this information in life. Thank you so much.

Master video presentation!! very very well done! and thank you.

Awesome video, thank you. It was really cool to see the systematic way of finding the Archimedean, Catalan and Johnson solids. Maybe you could talk about stellated polyhedra as well? I have looked at some stellations of the dodecahedron and the icosahedron and they are really beautiful but it is a bit unclear to me how to find them all and what are counted as proper stellations. I think they're so pretty that we even 3D-printed and assembled a small stellated dodecahedron as a prop for our university play.

I like these shapes - shapes are cool!

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.

your channel is so cool omg

things i learned from this: the geometrical name of a soccerball [2:49] how to make my favorite shape even outside of archimedians (basically my favorite polyhedra) [4:44] from squares only basically nothing else but here is the info requested great rhombicosidodecahedron triakis icosahedron hebesphenorotunda

My favorite Catalan solid is the 30-sided rhombic polyhedron based on the Golden Ratio because I figured out how to make it in Sketchup. It is closely related to the icosahedron and dodecahedron.

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

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

Just wow! Knowledge dense, but not confusing.

I love your videos ❤

Thank you for making a version of jan Misali's 48 Regular Polyhedra that respects its audience. I needed that.

Here are a few names of certain Platonic & Archimedean Solids: 1. Octahedron: Triangular Antiprism/Square Dipyramid 2. Icosahedron: Gyroelongated Pentagonal Dipyramid 3. Cuboctahedron: Triangular Gyrobicupola 4. Rhombicuboctahedron: Elongated Square Orthobicupola 5. Icosidodecahedron: Pentagonal Gyrobirotunda 6. Rhombicosidodecahedron: Elongated Pentagonal Orthobicupola BONUS: The pseudorhombicuboctahedron is called a elongated square gyrobicupola.

Best vid ever, i rewatched like 5 times

I'd love to see a video about tessellation of 3D space with golden rhombohedrons and what they build (such as the rhombic triacontehedron) and then combine that in the same video with looking at the dual polyhedra of the various related solids using the icosadodecahedron as the glue that fits the whole picture together. Quasicrystals are something a lot of people are interested in and these relationships are critical to quasicrystals because of the 5-fold symmetry (ie the golden ratio) and space-filling aspects of them. There's a sort of progression of the solids (via dual polyhedra?) that inspired Kepler to write mysterium cosmigraphicum and write the three laws of planetary motion based upon orbital resonance and its relationship to these geometries. I really feel like you could give these subjects a good treatment!

Glad you managed to show us all the crystal simetry cases with one video except for the pyritohedron

Very interesting. I love shapes