The ALMOST Platonic Solids

Omg platonic solids

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"

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.

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

Platonic solids Familial solids Romantic 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.

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.

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

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

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.

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

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

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

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

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