leahwrenn, 6 months ago Which aspect ratio do you prefer, for drawing the Pappus configuration on a torus? L to R: [1,1], [7,4], [3,1]. I'm going to print it next week. Maybe even in color on the super fancy 3D printer my university bought. Pappus on a torus: a 7 x 4 rectangle folded up Pappus on a torus: a 3 x 1 rectangle folded up
Which aspect ratio do you prefer, for drawing the Pappus configuration on a torus? L to R: [1,1], [7,4], [3,1].
I'm going to print it next week. Maybe even in color on the super fancy 3D printer my university bought.
Pappus on a torus: a 7 x 4 rectangle folded up Pappus on a torus: a 3 x 1 rectangle folded up
11011110, 6 months ago @leahwrenn The middle one
@leahwrenn The middle one
11011110, 6 months ago @leahwrenn Although it has a nice and much more symmetric drawing on the square torus:
@leahwrenn Although it has a nice and much more symmetric drawing on the square torus:
leahwrenn, 6 months ago @11011110 Yeah, that's a nicer embedding! Thanks! On the round torus: L is your embedding, R is Coxeter's Pappus configuration on the round torus, from a less-symmetric drawing on the square torus from Coxeter
@11011110 Yeah, that's a nicer embedding! Thanks! On the round torus: L is your embedding, R is Coxeter's
Pappus configuration on the round torus, from a less-symmetric drawing on the square torus from Coxeter
11011110, 6 months ago @leahwrenn I do like that Coxeter's is uncrossed. Maybe all three colors of lines can be made symmetric to each other on the hexagonal flat torus?
@leahwrenn I do like that Coxeter's is uncrossed. Maybe all three colors of lines can be made symmetric to each other on the hexagonal flat torus?
leahwrenn, 6 months ago @11011110 Maybe so, it'd be worth thinking about. I don't know how to lift a hexagonal torus onto a round torus, though (I'm using an implementation I found in a Bridges paper to do this one for rectangular tori—probably other people know how to lift parallelogram and hexagonal tori as well).
@11011110 Maybe so, it'd be worth thinking about.
I don't know how to lift a hexagonal torus onto a round torus, though (I'm using an implementation I found in a Bridges paper to do this one for rectangular tori—probably other people know how to lift parallelogram and hexagonal tori as well).
henryseg, 6 months ago @leahwrenn @11011110 This might be relevant for the hex torus: http://m.archive.bridgesmathart.org/2011/bridges2011-593.pdf
@leahwrenn @11011110 This might be relevant for the hex torus: http://m.archive.bridgesmathart.org/2011/bridges2011-593.pdf
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