/sci/ - Science & Math » Thread #14021487

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Anonymous Tue 28 Dec 01:05:47 2021 No.14021487 View Reply Original Report

Quoted By: >>14021497 >>14021542 >>14021585

Is there an equation that gives coordinates for vertices of a platonic solid or other solids like in the image? Image was obtain from sphere tessellation by icosahedron subdivision pdf.

Anonymous

Anonymous Tue 28 Dec 2021 01:08:56 No.14021497 Report

Quoted By:

>>14021487
No one really knows

Anonymous

Anonymous Tue 28 Dec 2021 01:22:56 No.14021542 Report

Quoted By: >>14021595 >>14021627

>>14021487
Mathematically, this is known to be an unsolved problem. In practice, the issue is usually approached by approximation with Monte Carlo methods.

Anonymous

Anonymous Tue 28 Dec 2021 01:36:43 No.14021585 Report

Quoted By: >>14021646

>>14021487
yes there are, I had to model a d-20 from scratch and I ended up using a cheat-like method of intersecting golden ratio rectangles to do it because the equations filtered me so hard. (I'm a machinist, not some fancy math dude)
They should be on wikipedia, or some other site still, I think it has to do with 3D symetry, like 2:5:6 symetry... I forget... it was a while ago.

Anonymous

Anonymous Tue 28 Dec 2021 01:39:58 No.14021595 Report

Quoted By: >>14021646

>>14021542
You can know the volume and everything but not the coordinates of the vertices?

Anonymous

Anonymous Tue 28 Dec 2021 01:50:15 No.14021625 Report

Quoted By: >>14021640

You know the coordinates for the vertices of a cube, and the vertices of an octahedron, don't you?

Anonymous

Anonymous Tue 28 Dec 2021 01:50:32 No.14021627 Report

Quoted By:

>>14021542
I believe you, but how can it be unsolved? Assuming you can know or assume the location of one corner you should be able to find the rest.

Anonymous

Anonymous Tue 28 Dec 2021 01:53:41 No.14021640 Report

Quoted By:

>>14021625
And you can get a regular tetrahedron using a subset of the vertices of a cube. Of the Platonic solids, it's just the dodecahedron and icosahedron that aren't obvious.

Anonymous

Anonymous Tue 28 Dec 2021 01:55:12 No.14021646 Report

Quoted By:

>>14021595
no, like I said in my other post >>14021585
there are formulas to find a inscribed sphere for all of them, it's only a matter of then using an unwrapped platonic solid with a known scale factor and then "re-wrapping" it to the outside sphere using polar-cartesian cord transforms.
easy peasy.
use this op.
https://rechneronline.de/pi/icosahedron.php

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