Over quarantine summer I started to make the archimedean solids out of paper and masking tape, but sadly I only finished 6 of the 13 before I ran out of steam, energy, and concentration. I ended up moving onto other hobbies such as painting and biking, but I wish my ADHD had let me stick to these.
@user-ou1us8tx9j5 ай бұрын
Ik how to make those out of paper but masking tape ? Did u use them to stick it or something else because I am a little confused
@zh8410 жыл бұрын
A lovely set of models. Thank you. The truncated icosahedron as you know is also the skeleton of the peculiar carbon molecule buckminsterfullerene.
@Qaptyl3 жыл бұрын
s o c k e r b o l l
@ithinkmallardsarecool58592 жыл бұрын
Lol
@galoomba55592 жыл бұрын
2:19 Correction: The vertices in both rings are the same, but the "polar" vertices (two squares) are distinct from the "equatorial" vertices (two octagonal rings)
@sandiandlee4 жыл бұрын
This was great to watch, the models are lovely
@henryseg10 жыл бұрын
Platonic and Archimedean solids.
@Rubrickety10 жыл бұрын
I didn't quite follow the hand-wavy bit about how one gets around the problem where truncation of certain vertices would seem to yield rectangles, but "done right" it yields squares.
@neilfred10 жыл бұрын
Okay, so truncate the cuboctahedron such that you do wind up with those rectangles. Now consider that version of the rhombicuboctahedron, centered at the origin and oriented such that the six squares are parallel to the XY, YZ, and XZ planes. Next, note that the set of edges that pass through the XY plane are the short edges of some of the rectangles, and note that they are all vertical. Since they are all parallel to each other, you can elongate all of them without disrupting any of the angles or other edges; so in particular you can elongate them just the right amount to make the rectangles into squares. Doing so turns the original squares into rectangles, but then doing the same for the YZ and XZ planes fixes those, so all the original squares now have edge length equal to the long edges of the rectangles, and the rectangles are all squares. Not sure how helpful that explanation is without any visual aid though...
@columbus8myhw7 жыл бұрын
Make the Johnson solids! Not all of them, only the ones listed under "others" on Wikipedia
@henryseg7 жыл бұрын
Here you go! shpws.me/Hmb8
@columbus8myhw7 жыл бұрын
Wow, that was fast. Thanks!
@lucascastillo93012 ай бұрын
my favorite group of5 and the rest of the 13 arc solids and the 13 cat solids and the 92 johnson solids
@Harlequin31415910 жыл бұрын
Great summary, and nice printouts! Follow-up question: if the rhombicuboctahedron has a variant that can be made by rotating one of its square cupolas (the elongated square gyrobicupola), what about the rhombicosadodecahedron and rotating one (or more) of its pentagonal cupolas?
@henryseg10 жыл бұрын
Yes, those are Johnson solids. See the Gyrate rhombicosidodecahedron for example.
@MattMcIrvin2 жыл бұрын
That solid exists but it is not as tricky a challenge to the definition of an Archimedean solid, because its vertices are not locally identical.
@liambohl2 жыл бұрын
Good point Matt. The family of gyrate rhombicosidodecahedra (rhombicosododecahedra with one or more rotundae rotated by an edge) each have some pairs of adjacent squares. In that way, they are like the triangular orthobicupola
@philopolymath8 жыл бұрын
Thanks to the life work of Frank Chester many more forms have been discovered... The 7 sided Chestehedron is but one of his path finding discoveries. He also gave us the method to unveil the complete family of complex solid forms. All forms exist between the Sphere & Cube
@columbus8myhw7 жыл бұрын
Unfortunately, the quadrilaterals of the Chestahedron are not regular, and so it is not an Archimedean solid.
@CesareVesdaniАй бұрын
What is the platonic and Archimedean solid that can be made using the greatest amount of faces, forming a near-spherical shape?
@aguyonasiteontheinternet2 күн бұрын
snub dodecahedron
@aSeaofTroubles9 жыл бұрын
beautiful presentation!
@wolfstar38834 жыл бұрын
Make the 92 Johnson Solids next!
@theodriggers5492 жыл бұрын
And the 13 Catalan solids (duals of Archimedean solids)
@crinklecake532 жыл бұрын
i do like these, but personally much more of a fan of the duals to the archemedian solids, the catalan solids.
@dogsareawesome919710 ай бұрын
The rhombicosidodecahedron is my favorite shape, its the perfect mix of round and blocky
@funwithtommyandmore6 ай бұрын
Personally I'm more into the pontoremeyotoqatonodexofantopoloyotrahedron. Easy to get mixed with the rotlokoizooxloqatolatoronopoloitonosomonidolopilokalokanoyotctafantohedron.
@dogsareawesome91976 ай бұрын
@@funwithtommyandmore fanum tax?
@stringertothefinger2 ай бұрын
@@funwithtommyandmoreidk man .. if those words are real, then Terrence Howard is onto something. Damn those Anunnaki and straight lines
@alexgabriel54234 жыл бұрын
Would you kindly give an introduction to Aristotle s philosophy behind the solids of his imagination...what was he thinking about them?
@Kroggnagch Жыл бұрын
Alright this is cool shit. Subscribed.
@johnnydarling8021 Жыл бұрын
6:35 That’s a classic soccer ball!
@tristenarctician6910Ай бұрын
Would there be any more shapes possible if the regular polygon faces requirement was removed, but still needed all vertices be the same?
@robertbell3578Ай бұрын
These are great looking models I'd love to know how you made them? Did you create moulds?
@henrysegАй бұрын
They are 3D printed, in selective laser sintered nylon.
@Jujuoak3 жыл бұрын
I can tell that this video is very informative, but I’m having a hard time understanding this haha
@zakkdavis17047 жыл бұрын
good video ..I'd like to have those shapes ..geometry is good vibes
@misteribeiro2 жыл бұрын
all i know is the tetrahedron " structurally speaking " outlasts them all
@gloria7641 Жыл бұрын
use polyhedrons to stack them
@SquirtleSquad443 Жыл бұрын
6:37 me trying to draw a soccer ball (football) but I keep forgetting what shape the pieces are
@glorianegrette2717 жыл бұрын
traduzca en español como elaboro esas figuritas o que maquina se utiliza por favor informe donde las consigo en colombia
@columbus8myhw7 жыл бұрын
Traduje tu comentario a inglés. "Please translate to Spanish how to make these figures or what machine is used; let me know where to get these in Colombia."
@swinde9 жыл бұрын
Can a sphere be described as a regular solid with an infinite number of faces? I know that it is problematic because a circle can be described as a regular polygon with an infinite number of sides also. So if the circle already has an infinite number of sides, how can a sphere be constructed? Also, How can there be more than one circle? How can it even be observed? It can be constructed with Euclidian mathematics yet cannot be adequately defined. Just wondering? I am pretty sure this is why the value of pi cannot be precisely calculated.
@henryseg9 жыл бұрын
You could say that a sphere is the _limiting shape_ of a certain sequence of regular polyhedra (and to be pedantic, we have to be careful about what kind of limit we are taking). The circle can certainly be defined - it is the set of points at a given distance from some center point. And pi can be precisely calculated - take the ratio of the length of the circumference to the length of the diameter. You are right that we cannot write pi down as a decimal expansion of finite length, but that doesn't mean that we don't know precisely what it is.
@fauddin27127 жыл бұрын
excellent
@geoffphil Жыл бұрын
Where can I get a set of these polyhedra? Great Video thankyou.
@henryseg Жыл бұрын
Links in the video description!
@maverickvalderrama7 ай бұрын
Gimmie Catalan solids
@geoffphil Жыл бұрын
Where can I get a set if these polys? Great video thanks.
@theodriggers5492 жыл бұрын
Have you seen the truncated rhombicosidodecahedron?
@mathmachine42662 жыл бұрын
Why don't the infinite number of prisms and antiprisms fit in here?
@henryseg2 жыл бұрын
Only because they are explicitly ruled out to get a finite collection. There's more of a debate over why the en.wikipedia.org/wiki/Elongated_square_gyrobicupola is not included.
@viratwisetsingh26596 жыл бұрын
Elongated square bicupola? Is rhombic cuboctahedron
@KlaxontheImpailr2 ай бұрын
Has anyone tried to make 4 dimensional Archimedian solids?
@aguyonasiteontheinternet2 күн бұрын
idk look it up on wikipedia or smth seriously there’s a whole page there
@theodriggers5492 жыл бұрын
Truncated cuboctahedron = great rhombicuboctahedron Truncated icosidodecahedron = great rhombicosidodecahedron
@theodriggers5492 ай бұрын
(topologically)
@SlashCrash_Studios2 жыл бұрын
Something Something Muoctahedron
@akhilcleatus79384 жыл бұрын
😍😍😍
@pablesm4 жыл бұрын
Truncated icosahedron is soccer ball
@okboing2 жыл бұрын
are platonics part of the archimedians?
@henryseg2 жыл бұрын
Usually the platonics are not included in the archimedians, but it depends on your definitions.
@badchessplyr5 жыл бұрын
from where can i buy these cool looking solids ?
@henryseg5 жыл бұрын
Links are in the video description.
@austincollier87739 жыл бұрын
what type of 3d printer are you using?
@henryseg9 жыл бұрын
austin collier I use shapeways.com's "White Strong & Flexible" material, which is a nylon plastic printed using a selective laser sintering machine.