-
-
Replying to @graveolens @Sabetta_
In this setting wouldn’t each “face” be only able to have one vertex.
1 reply 0 retweets 0 likes -
Take the vertices of a tetrahedron -- I think I was thinking of the tattoo image, start with hyperbolic helicoids between pairs of vertices, and the two fitting together (maybe touching or deforming one another like modular paper art)
1 reply 0 retweets 0 likes -
all Platonic solids have an even number of vertices, so take pairs of them and link with hyperbolic helicoids (maybe they all have uniform charge distributions so repel one another?)
1 reply 0 retweets 0 likes -
and each helicoid might be distorted a little bit to make room for the others it's intercalated with. ... weaving with rotini
1 reply 0 retweets 0 likes -
Replying to @graveolens @Sabetta_
I would love to see the object you describe! Though as soon as you distort the surfaces they are no longer really helicoids.
2 replies 0 retweets 0 likes -
Not quite the same thing, but you might like these animations of some assemblies of locally helicoid-like surfaces from Ken Baker https://sketchesoftopology.wordpress.com/2008/11/24/the-jvhm-open-book/ …pic.twitter.com/qpJ2pCsnmg
3 replies 1 retweet 9 likes -
There is a theorem by Colding and Minicozzi that says all minimal surfaces are made from pieces of helicoid and pairs of pants. https://www.pnas.org/content/103/30/11106 … Most minimal surfaces can be decomposed into nonlinear sums or products of helicoids.
2 replies 1 retweet 4 likes
Like, what I had in mind started from the last image here: http://wordpress.discretization.de/ddg2016/2016/05/17/tutorial-4-hyperbolic-helicoids/ … /oh, couldn't you put another one so that the points on the sphere (in one embedding) were a tetrahedron?/
-
-
Replying to @graveolens @Sabetta_ and
I think I first thought of papercraftish hyperbolic helicoids like
@Gelada 's interlinked paper constructions with vertices per platonic solids. (The next idea was a little weirder: if there's space enough for the vertices, isn't there space enough for translates of them?...1 reply 0 retweets 0 likes -
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.