The globe, the tetrahedron and the number "6"

The largest regular tetrahedron inside a sphere draws out the latitude 19,47 deg when rotated.
The Earth’s tropics of the cancer and the capricorn are at 23.4394 degrees, not that far and considering it’s not a sphere anyway, pretty close.
Now, when we draw one such tetrahedron we’d draw the other turned upside down, sharing the same center. When we now view this from the side, we see the 2D outline of the Star of David.
Here the number “6” is clearly in view, when connecting the Star of David’s vertices we are left with the hexagon.

probably better (or not) if you explain what you want to say in a method other than riddles…

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Well, no riddles, just some notions that provoke more remarkability for Platonic geometry. One more being that there is statistical emphasis to certain things on Earth that are found near those Tropics near 19,47 degree latitude, I mean, other things than what clearly arise from the definition of Tropics… Also, clearly nature just loves the number 6.

futility to the sixth degree

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Actually the latitude 19.47 does include such things as the largest active volcano on earth in Hawaii, Jupiter’s Red Spot, and Olympus Mons on Mars, for example.

And the number 6 is reflected in nature with such things as snowflakes, beehives and the benzene ring.

But the question does remain, why bring this up? No disrespect intended.

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I don’t understand such a loud craving for the why of it.
As I see it these are fundamental symmetries found on our globe and as mentioned, some other globes as well. We live on a globe so why not bring this up?
Also any religious or spiritual connotations arising from these symmetries come after the fact that they exist in nature.

True, but, to paraphrase The Register’s regular refrain “where’s the audio angle?” :slight_smile:

El Reg

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To be fair, I am known for sometimes rambling off topic on this forum too :wink:

I’m guilty of doing this as well.

That having been said, this may not be the time for bringing up a topic (sacred shapes and 19.47) that is related, even tangentially, to the Star of David and the founding of Israel.


Glad you asked! I’m currently designing a tetrahedral omni-directional loudspeaker!

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Ha! Now we’re talkin’ :slight_smile:
how many drivers in it?

Four, there’s need for a series-parallel connection to keep impedance in check. I was originally thinking of three, without a bottom face driver but then realized it hurts both the impedance and the omni-directionality.

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Have you thought of expanding the concept and design to a dodecahedron (12-sided a la Design Acoustics with their D12 c.1973) ?


Well, research into regular polyhedra certainly shows some benefit for the dodecahedron over the tetrahedron in dispersion but no, at least not yet I can’t bother the woodworker with such a shape as the dodecahedron. Also, can’t afford that many drivers of the type I want, nor could I conveniently give them enough internal volume.
Also at higher frequencies the tetrahedron seems to smooth out dispersion better than an equal-midradii dodecahedron.

As I understand the dispersion characteristics of polyhedra equipped with drivers is more so dependent on the angles than the exact shape itself. The edges are not useful for dispersion, so really the ultimate solution might be a sphere with the drivers arranged on its surface with the angles of the regular tetrahedron.

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A long time ago in a decade far away I played lead guitar on a “space rock” band. All good fun, and the lead singer made some pyramid shaped speaker “wedges”.
He did a beautiful air brush paint job on them and they were pretty big,
But they had very limited volume (in litres) due to the shape, given the base was so large so we stopped using them, just put them on stage still because they looked so cool :slight_smile:

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We are way over my head (picture a carpet) when it comes to acoustics and loudspeaker design.

If I lived in a barn and had an obscene amount of money I’d love to have these. Maybe.

Lift the carpet previously mentioned and notice the dust. That’s my musical talent. I have great admiration and a lot more envy for those who do have that talent. I’m a listener not a doer.