March 21, 2023, 04:33:49 AM
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### Topic: Octahedron Uses  (Read 389 times)

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#### Enthalpy

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##### Octahedron Uses
« on: January 29, 2023, 11:06:16 AM »
Hi everyone and everybody!
I ignore if this thingy has some use, but at least it's puzzling.

The well-known octahedron depicted below lets an even number of faces and edges converge to each apex. It's also regular, as all faces are identical triangles. It's the only regular solid with the even property.
Octahedron - Platonic solid at Wiki

We can assign "+" and "-", or "1" and "0", or "North" and "South" alternately to adjacent faces all over the surface of the octahedron. Just as we can assign "Arrival" and "Departure" alternately to adjacent edges at every apex, and these can be current flows that create magnetic fluxes in and out through the faces.

Consider the three equatorial planes that separate the octahedron in two pyramids. By symmetry if all currents are identical, the induction perpendicular to the plane at its center is zero. This holds in three directions, so the induction vector is zero at the center. The induction increases towards the North and South faces, and also towards the edges (so to say East and West poles: a vector field can vary from North to South without passing by zero, its direction succeeds where a mere sign fails). Only the apices directions bear no induction.

The faces can be permanent magnets, where holes and slits don't hurt. Or the edges can be conductors, superconductors, cold conductors (aluminium around 20K)
chemicalforums on 24 Jul 2022 and 26 Jul 2022

Does an induction that increases outwards have uses? Maybe it could make a trap for charged particles if the apices don't leak too much, say if the low-induction channels are narrower than the particles' movements.

Do less regular geometric solids alternate North and South adjacent faces? The soccer ball doesn't.

Marc Schaefer, aka Enthalpy

#### Enthalpy

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##### Re: Octahedron Uses
« Reply #1 on: January 31, 2023, 07:14:33 PM »
If someone wishes more faces, he can split every face of the octahedron in four as depicted below. And repeat as desired. This keeps the alternating North and South faces.

The apices can reside all on one sphere if desired. I suppose the faces aren't absolutely identical any more.

Marc Schaefer, aka Enthalpy