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

s o c k e r b o l l

Lol

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.

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...

Make the Johnson solids! Not all of them, only the ones listed under "others" on Wikipedia

Here you go! shpws.me/Hmb8

Wow, that was fast. Thanks!

Yes, those are Johnson solids. See the Gyrate rhombicosidodecahedron for example.

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.

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

Unfortunately, the quadrilaterals of the Chestahedron are not regular, and so it is not an Archimedean solid.

snub dodecahedron

And the 13 Catalan solids (duals of Archimedean solids)

Personally I'm more into the pontoremeyotoqatonodexofantopoloyotrahedron. Easy to get mixed with the rotlokoizooxloqatolatoronopoloitonosomonidolopilokalokanoyotctafantohedron.

@@funwithtommyandmore fanum tax?

@@funwithtommyandmoreidk man .. if those words are real, then Terrence Howard is onto something. Damn those Anunnaki and straight lines

They are 3D printed, in selective laser sintered nylon.

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."

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.

Links in the video description!

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.

idk look it up on wikipedia or smth seriously there’s a whole page there

(topologically)

Usually the platonics are not included in the archimedians, but it depends on your definitions.

Links are in the video description.

austin collier I use shapeways.com's "White Strong & Flexible" material, which is a nylon plastic printed using a selective laser sintering machine.

JQ