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# surface connectors

alternative to magnets
 (+2) [vote for, against]

Space filling blocks are a fun toy.

Typically space filling blocks are rectangular/cubic. On a horizontal surface the blocks stack nicely because: a) the top surfaces of the blocks are also horizontal, and b) gravity is perpendicular to this.

I am interested in non-cubic space filling blocks. Non-cubic space-filling blocks do not have the benefit of gravity sticking the blocks together. The blocks must be connected by another mechanism.

I was first interested in rhombic dodecahedrons. My interest has now moved to golden rhombohedrons. Golden rhombohedrons are interesting because they can be stuck together to form rhombic dodecahedron and rhombic triacontahedrons. They are also interesting because they can be stacked in 3 dimensions in a non-periodic configuration, thus making them a good model of quasi- crystals.

I have discovered there was a building toy with the shapes of golden rhombohedron called "Rhombo". Each face of each block contained a magnet, allowing the blocks to be connected and thus forming interesting structures. As far as I can tell it is no longer for sale.

Using magnets as the connector for these blocks is an obvious choice since it allows the faces of the blocks to be smooth so the blocks can be slide together. This is especially important when putting in the last piece in a concave space (e.g. the last piece in a rhombic triacontahedron).

Anyway, I thought it would be interesting to come up with a surface connector that had similar functionality as magnets.

So my idea is a surface that contains a rotating connector. The rotating connector is attached to a spring that, when activated, causes the connector to move from a flat orientation to an angled orientation (see illustrations).

Two connectors when placed against each other, will rotate around approximately the same axis, and connect.

The connectors are initially held in a flat configuration by a resilient finger (not shown in illustrations). The resilient finger is just strong enough to resist the pull of a tension spring. When pressure is applied to the surface of the connector (by another connector placed on top), this disengages the resilient finger, and the tension spring pulls the connector into the angled configuration.

One surface will require 2 (or more) of these connectors which will form a 'dovetail' configuration. With enough force the connector can be pulled apart. The connectors can then be reset by pushing the connectors into the resilient fingers in the flat configuration.

 — xaviergisz, Mar 09 2021

Rhombo http://rhombo.com
golden rhombohedron magnetic blocks [xaviergisz, Mar 09 2021]

Golden rhombohedron https://mathworld.w...enRhombohedron.html
[xaviergisz, Mar 09 2021]

Rhombic dodecahedron https://en.wikipedi...hombic_dodecahedron
[xaviergisz, Mar 09 2021]

Rhombic triacontahedron https://en.wikipedi...bic_triacontahedron
[xaviergisz, Mar 09 2021]

illustration 1 https://i.imgur.com/iX3IXXw.png
[xaviergisz, Mar 09 2021]

illustration 2 https://i.imgur.com/ShkLtFs.png
[xaviergisz, Mar 09 2021]

illustration 3 https://i.imgur.com/qsT88Ji.png
[xaviergisz, Mar 09 2021]

How did I not know about golden rhombohedrons?!
As for your connectors, I've pondered the same dilemma (but pertaining specifically to connecting identical robots together, although I'm after rotational symmetry).
Perhaps if the connector had a mass at the "non-spring" end, then if you "whack" them together, the masses will activate the connector when the rest stops moving on impact.
If you set up your hinge & spring so it's an "over-centre" alignment (only just past in the "flat" position, obviously), you can do away with the "fingers" of your design.

Immediate [+] for bringing golden rhombohedrons to my attention.
 — pertinax, Mar 10 2021

 Okay, wow, I get it, it's totally cool... but, if somebody could put the following;

 "A golden rhombus is a rhombus whose diagonals are in the ratio p/q=phi, where phi is the golden ratio."

 ...into something I don't need to spend a decade learning that would be really great.

 I love the rotate shape thing on those links by the way.

...oh and,
//The resilient finger is just strong enough to resist the pull of a tension spring.//
is officially
[marked-for-tagline].
 — 2 fries shy of a happy meal, Mar 10 2021

It's just saying if a golden rhombus (diamond shape in more colloquial terms) has a width (from the two opposite corners) of 1cm then the length (from the two other opposite corners) will be 1.618cm. If it has a width of 10cm then the length will be 16.18cm, etc.
 — xaviergisz, Mar 10 2021

Cool... why 1:1.618 as a scale?
 — 2 fries shy of a happy meal, Mar 10 2021

 What makes it golden?

 Sorry it's been a long day. Don't sweat it I will look it up.

That's just a lot of terms to hear for the first time.
 — 2 fries shy of a happy meal, Mar 10 2021

 The golden ratio, phi, (for some reason normally given as "1.618..." (ie. bigger than 1) instead of the usual "ratio" value of less than 1...) is found in various places in nature, as well as (apparently) "aesthetically pleasing". But that's just artsy waffle... It has the unique property that 1/phi = phi - 1, AND (actually mathematically equivalent) phi^2 = phi + 1. ie: 1/1.6180339887 = 0.6180339887 and 1.6180339887^2 = 2.6180339887 It's also the limit of the ratio of 2 consecutive values of the Fibonacci sequence. (Yes, I'm a maths geek. Among other things, I did an essay/study of Fibonacci for a 3rd-year university maths paper...)

 PS: "phi" is the Greek letter phi, normally written in Greek...

PPS: phi = (1+sqrt(5))/2
(the easy way on a calculator is 1.25, sqrt, +, .5)

Huh. hmmmm
 — 2 fries shy of a happy meal, Mar 10 2021

Too much? Or too "geek"?

 Another way to imagine it is this: imagine a line divided into two unequal parts, where the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller part.

Phi is that ratio.
 — pertinax, Mar 10 2021

Yeah; I forgot about that definition...
Mathematically: (assuming a<b) a/b = b/(a+b)

 //Too much? Or too "geek"?//

 No it's great. Thank you.

 //the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller part.//

 Aha! I can see it now.I frustrated the hell out of my teachers in school because I could only learn visually at that time so although math was my worst subject and I failed miserably I totally aced things like trigonometry and geometry because I could see them in my head. Bring my mark back up to a nice 52% or so overall so I could attend the next grade.

 Except circle math. I never really understood exactly what Pi was until I watched a three second gif a few years ago.It was just another number to be memorized by rote.

Seriously... time-machine, past guidance-counselors, ass-kickings all-round.
 — 2 fries shy of a happy meal, Mar 11 2021

Okay maybe sternly worded memo's.
 — 2 fries shy of a happy meal, Mar 12 2021

 //I was first interested in rhombic dodecahedrons. My interest has now moved to golden rhombohedrons. Golden rhombohedrons are interesting because they can be stuck together to form rhombic dodecahedron and rhombic triacontahedrons. They are also interesting because they can be stacked in 3 dimensions in a non-periodic configuration, thus making them a good model of quasi- crystals.//

I was struck by 2 things in this paragraph. How "Deliciously nerdy" it sounds AND "That sound's interesting to me".
 — AusCan531, Mar 12 2021

 Squeeze together connection system using lower air pressure? but if the shapes are too interlocking, it might not be too easy to get the matching faces apart.

But there's always the microwave. or fridge.
 — wjt, Mar 13 2021

Also, possibly, with deep pockets, an unseen Electrical Discharge Machining pairing brick surface. Enough to beat gravity but shaped to slide.
 — wjt, Mar 13 2021

 [annotate]

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