
#1
Dec2307, 10:16 PM

P: 15,325

It is with mixed success that I finish my third attempt at what I hope is the world's first realworld (i.e. not computerrendered) tesseract, or hypercube.
It started last spring while I was bored in a jobhunting class. I was studying my MeyerBriggs results, and the chart that divides all people into one of 16 groups. I wanted a chart that could represent all 16 types in one symmetrical arrangement If there were only two properties, all combinations could be represented in a simple table: Introverted/Extroverted Sensing/iNtuiting
Introverted/Extraverted Sensing/Intuiting Thinking/Feeling
On this webpage, I'm forced to flatten it to 2 dimensions, and have the third stick out the side. This produces an unintentional bias toward one property over the others. In the above example, Sensing/Intuiting is singled out as two tables. But as a cubic table, I can represent all three properties in their correct relationship to each other. All I have to do is flip the cube so I'm looking at the properties I want. Property 1: columns Property 2: rows Property 3: depths But ... with four properties, you can't represent them all at the same time in correct relation to each other. Jjust like stacking two 2D tables got me a 3D cubic table, I'd like to be able to stack two 3D cubic tables to make one 4D table Introverted/Extroverted Thinking/Feeling Sensing/Intuiting Judging/Perceiving
The fourth property is represented by a fourth dimnesion in the table. Property 1: columns Property 2: rows Property 3: depths Property 4: ? Now, since the physical world can't actually represent a 4th dimension, it gets squashed. This squashed layer can be represented by a 4th squahsed "direction": layers. Inner and outer. What I want to be able to do, ultimately, is rotate the tesseract as I please, like this: Thus begins my quest for a realworld tesseract. 



#2
Dec2307, 10:23 PM

P: 15,325

My first attempt is with chemistry building blocks. The vertices are all carbon atoms.
I didn't work out because the lengths of the sides have to change. The "struts" that join the inner and outer cubic tables are shorter. But this model doesn't do that; the structure doesn't collapse properly; it won't easily turn inside out. 



#3
Dec2307, 10:31 PM

P: 15,325

This one is built with great pains (trust me on this) to make contractable/expandable struts like pistons (32 struts, each made of two pistons for a total of 64).
This had a very interesting lesson: when we allow the device to do what it needs to do to rotate, it now does it too easily. All 32 struts must change length at the same time. This model would not hold its shape long enough to even get it looking like a tesseract, it just collapsed like so many sticks in a game of pickup sticks. I couldn't even set it up to take the pic! You can see the outer cube, the the inner one just falls flat. I need a model that is selfsupporting. 



#4
Dec2307, 10:40 PM

P: 389

Real world tesseract
I was going to suggest magnetic sticks with ball bearing vertices but it doesn't look like it's working,




#5
Dec2307, 10:42 PM

P: 15,325

My next attempt, which I've just finished, is made of even more permanent material, and more exacting measurements and its solid structures provide some support so that it does not completely collapse in on itself.
The basic subunit is a cube with four corners truncated and a joint in the face of each. (The cubes, all 16 of them, with their 4 truncated vertices apiece, have been cut and sanded to within less than 1mm) The subunit cubes are joined by stretchy elastic cord. Interestingly, while a a cube has three edges to every vertex, a hypercube has 4 edges to every vertex. One sideeffect of this is that every subunit has an even number of cords attached to it. That means no subunit has an end of the cord, the yare all "passthrough". That entire elastic cord is one single piece, threaded through out the entire model. In fact, it has zero ends  it's a loop. That aside though, I'm still having some troubles. It still doesn't easily transform from one shape to another. Too much friction and too much looseygoosey. I have yet to create one that smoothly transofmrs from one shape into the next without a tremendous amount of awkward, showstopping fiddling. Also, I have not yet managed to get the thing to open a portal to an alternate dimension, making me rich and famous beyond my wildest dreams of avarice. I continue on my quest. 



#6
Dec2307, 11:43 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

I would have suggested hollow, lowfriction, telescoping rods with an internal, lowstiffness spring.




#7
Dec2407, 04:11 PM

P: 15,325

The lowfriction thing was what I worked very carefully on. That was the rationale for the hours of precision work. Strangely, it turned out to be the wrong thing. Those pistons have zero frction. So little that I can't even get the thing to stay put; I basically have to support every single strut at all times or it collapses into what you see. (And I don't mean standing on its own, I mean when I'm supporting it in my hands, I can only hold a dozen or so struts. Any that I'm not holding just flop like an old woman's funbags.) That's what all that tape is on there for in the pic above; it's there to add friction. As for the spring, that's pretty tricky. Sometimes it needs to have compression tension, soemtimes it needs expansion tension. That was the rationale ofr the Mark III. The solid shape provides an automatic spacer  two forces in opposite directions (so that the spring can always be compression.) 



#8
Dec2407, 09:26 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

I was thinking that the spring would be good because it has a natural length that it'll want to retain. That would prevent the kind of collapse that happened with MkII. Also, some friction is good, as a damping force. Ideally, you'd want the system to be optimally damped.



Register to reply 
Related Discussions  
real world problem  General Engineering  2  
Mathematics and the real world  General Math  10  
Got a real world problem here ..  Differential Equations  2  
the real lost world  General Discussion  0  
The real question in real world!  Introductory Physics Homework  4 