Shiny Plexiglas Polytope

Today I am publishing something that is extraordinarily well-thought-out since it has been three years since I started this post… 😉 But it is also something I am especially proud of — so I wanted to do this right. 🙂

At some universities in Germany there is the tradition of doctoral hats. Wikipedia and Google offer some pictures; only those I know (from Darmstadt, Berlin, and Braunschweig) are much cooler since they are decorated with things — often in form of small riddles — related to the PhD candidate and/or his/her work.

At TU Berlin someone invented the analogous tradition of a habilitation necklace. As far as I know, this was the first ever exemplar:

Dodecahedron

I found this pretty cool, the idea and the implementation! So when a good friend of mine habilitated at TU Darmstadt in April 2014, I thought we should also build one for him.

Here’s what I made:

Permutahedron Permutahedron glowing Plexiglass Permutahedron

It turned out to be a really fun project. In this post, I want to explain how I build this thing.

The idea

First I, abstractly, decided to somehow build the following: (This is interactive and also contained in my math gallery.)

Discrete geometers call these guys polytopes. Here we have an octahedron inside a 3-permutahedron. Geometers might find this configuration interesting in its own right but this post is not about the math.

Then I decided to build it from Plexiglas with LEDs in the red points (i.e., the lattice points) and only then I began thinking about the project’s feasibility. 😉

The material

I needed eight hexagons, eight squares and eight triangles. (For the discrete geometers among you, in case you wondered: This includes two additional squares to connect the two polytopes.) Moreover, I needed 38 LEDs in total — six for the inner octahedron and 32 for the outer permutahedron. Since I wanted to have different colors for inner and boundary lattice points, I got white and blue LEDs.

Cutting and grinding

Although many people seem to use the name Plexiglas to mean any sort of acrylic glass, it is actually a trademark by the Rohm Company — and I wanted to use the real thing. (Since I have connections to someone working at Rohm, I could easily get my hands on it.)
Annoyingly, most people didn’t seem to get that. So whenever I asked for advice in the hardware store, they would tell me nonsense. If other acrylic glass really has all those problems I was warned about, I am extremely happy I used real Plexiglas. E.g. it never melted, no matter what I did to it. (I was actually told to use sandpaper in order to chamfer the edges — I replied that I did not intend to spend the next three years sandpapering…)

I printed a layout for the shapes I needed and then cut the Plexiglas using a multitool with a sawing blade. (I tried scoring and breaking but it turned out to be a BAD idea.)

Multi Tool Saw

Afterwards I used a rather coarse grinder plate to chamfer the edges to the appropriate angles.

All the time I wore these:

Safety Glasses

The glue

The clou was the glue (pun intended). It turns out there is special Plexiglas glue, which is basically like liquid Plexiglas and hardens in UV light (i.e., the sun).

This is easily the coolest glue I ever worked with. It smells horribly — and by this I mean really, really horribly (I had to stretch my arms complete in order to get it as far away from my face as possible.) — but it does glue amazingly.

Plexiglass pieces Plexiglass pieces Plexiglass pieces

The electronics

I have studied physics for a few semesters, so I do understand the basic laws of electronics, but I had never really worked with LEDs before. And until this point I hadn’t put any real thought into the layout. So I did some research:

I learned that you should never use an LED without a resistor. Moreover, in a parallel circuit every chain should of course have its own resistor. This was a big problem (for the looks). I neither wanted to have myriads of wires leaving the polytope (since I wanted to minimize the amount of wire inside) nor wanted I to have a lot of resistors inside the polytope.
I discussed with other people how to get a higher voltage power source and considered using a step up. Someone also told me that it was not going to work at all…

Then I started to experiment:
Since I had ordered the LEDs in China I had no specs for them. After consulting Wikipedia and some experiments with a 9V-battery and a multimeter, I decided that their forward voltage drop was something in the area of 3.3V. (With a 9V-battery I could light four of them rather dimly or three very brightly.)

Encouraged by these attempts, I decided to just put it all onto a breadboard (without any resistor) and see what happens. It turned out that it worked! 🙂 (I know you shouldn’t do this but since my circuit is powered by a battery I do not expect any drastic peaks in voltage.)

Experimenting with LEDs on a breadboard

Experimenting with LEDs on a breadboard

Experimenting with LEDs on a breadboard

I only wondered for how long. My most optimistic calculations gave me something around 2.5 hours. (The LEDs draw 20mA max and I had twelve parallel chains on the board. The battery should have had a capacity of 500-600mAh.)
I cancelled the experiment when the lights were still on (but a little dimmer) after 20 hours. If someone understand this, please comment!!

Assembling it

After I had the vague idea for the layout of the wiring, I started connecting the LEDs.
I knew I’d have to put them under some stress when assembling the whole thing, so I refrained from soldering them together. Instead I bought transparent heat sleeves which did the job just fine.

First, I manufactured chains of three LEDs each (and one consisting of two LEDs and one 220R resistor).

LED chains LED chains

I also got some copper wire as the common anode and cathode, respectively, for my 13 chains.

Then I tried to figure out how to get it all into the polytope…
At some points I felt I needed another set of fingers but then there wasn’t even enough space for those I’d got…

Wiring chaos inside the polytope

The final touch

There were going to be more things attached to the necklace. One of them was a memory module (part of a riddle), which I thought I might use to hide the battery case behind. I drilled some holes into the module (one for the switch and one to screw the battery case to it).

Memory module with battery case

Finally, I got a chain in the hardware store and attached the polytope and the battery module to it.

Polytope attached to chain

And here’s the finished necklace with all riddles attached.

finished necklace

Links: Montagsfreuden, NoSewMonday, Creadienstag, DienstagsDinge, Handmade on Tuesday

  1. Mila Liebe October 23, 2017 12:25

    Liebe Silke,

    eine wundervolle Tradition und ein tolles Projekt. Schon wieder mein Wissen erweitert. Einen sehr spannenden Blog hast du, ich gehe jetzt mal weiterstöbern.

    Alles Liebe

    Mila

  2. sjoe November 1, 2017 11:15

    von der Tradition habe ich noch nie gehört, aber genial, was du da fĂŒr ein Teil gebastelt hast!
    außerdem wieder gelernt, dass es “echtes” und “unechtes” Plexiglas gibt. gut zu wissen!

    LG
    sjoe

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                [post_title] => Schlupfvariablen
                [post_author] => 2
                [post_date] => 2013-01-06 19:27:16
                [year] => 2013
                [month] => 1
                [post_type] => post
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        [107] => stdClass Object
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                [post_name] => homework
                [post_title] => Homework
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                [post_date] => 2013-01-06 19:17:12
                [year] => 2013
                [month] => 1
                [post_type] => post
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        [108] => stdClass Object
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                [post_date] => 2012-10-28 00:32:43
                [year] => 2012
                [month] => 10
                [post_type] => post
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        [109] => stdClass Object
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                [slug] => design
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                [post_name] => ismp-bingo
                [post_title] => ISMP-Bingo
                [post_author] => 2
                [post_date] => 2012-09-22 20:34:00
                [year] => 2012
                [month] => 9
                [post_type] => post
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        [110] => stdClass Object
            (
                [slug] => design
                [ID] => 1025
                [post_name] => diskrete-optimierung-animiert
                [post_title] => Diskrete Optimierung animiert
                [post_author] => 2
                [post_date] => 2012-09-22 19:40:33
                [year] => 2012
                [month] => 9
                [post_type] => post
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        [111] => stdClass Object
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                [post_date] => 2012-08-10 22:44:23
                [year] => 2012
                [month] => 8
                [post_type] => post
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        [112] => stdClass Object
            (
                [slug] => design
                [ID] => 777
                [post_name] => diskrete-optimierung-logo
                [post_title] => Diskrete Optimierung: Logo!
                [post_author] => 2
                [post_date] => 2012-08-08 15:06:41
                [year] => 2012
                [month] => 8
                [post_type] => post
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        [113] => stdClass Object
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                [post_name] => tropical-oriented-matroids-in-3d
                [post_title] => Tropical Oriented Matroids in 3d
                [post_author] => 2
                [post_date] => 2012-07-24 18:24:41
                [year] => 2012
                [month] => 7
                [post_type] => post
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        [114] => stdClass Object
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                [post_name] => leinwand-gastebuch
                [post_title] => Leinwand-GĂ€stebuch
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                [post_date] => 2012-07-02 10:31:45
                [year] => 2012
                [month] => 7
                [post_type] => post
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        [115] => stdClass Object
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                [slug] => math
                [ID] => 1172
                [post_name] => the-polymake-logo-in-3d
                [post_title] => The polymake logo in 3d
                [post_author] => 2
                [post_date] => 2012-06-26 18:15:54
                [year] => 2012
                [month] => 6
                [post_type] => post
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        [116] => stdClass Object
            (
                [slug] => tech
                [ID] => 1166
                [post_name] => a-three-js-interface-for-polymake
                [post_title] => A three.js interface for polymake
                [post_author] => 2
                [post_date] => 2012-06-24 18:03:24
                [year] => 2012
                [month] => 6
                [post_type] => post
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        [117] => stdClass Object
            (
                [slug] => diy
                [ID] => 861
                [post_name] => leinwand-namensschilder
                [post_title] => Leinwand-Namensschilder
                [post_author] => 2
                [post_date] => 2012-06-08 14:03:05
                [year] => 2012
                [month] => 6
                [post_type] => post
            )
    
        [118] => stdClass Object
            (
                [slug] => design
                [ID] => 1133
                [post_name] => t-shirt-design-fusball
                [post_title] => T-Shirt-Design: Fußball
                [post_author] => 2
                [post_date] => 2012-05-24 16:01:16
                [year] => 2012
                [month] => 5
                [post_type] => post
            )
    
        [119] => stdClass Object
            (
                [slug] => diy
                [ID] => 1153
                [post_name] => cookie-monster-muffins
                [post_title] => Cookie Monster Muffins
                [post_author] => 2
                [post_date] => 2012-04-24 17:19:15
                [year] => 2012
                [month] => 4
                [post_type] => post
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        [120] => stdClass Object
            (
                [slug] => diy
                [ID] => 1221
                [post_name] => my-thesis-in-acrylic-paint
                [post_title] => My Thesis in acrylic paint
                [post_author] => 2
                [post_date] => 2012-02-28 09:30:14
                [year] => 2012
                [month] => 2
                [post_type] => post
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        [121] => stdClass Object
            (
                [slug] => design
                [ID] => 1084
                [post_name] => komm-doch-mal-wieder
                [post_title] => Komm doch mal wieder ...
                [post_author] => 2
                [post_date] => 2012-02-23 11:41:07
                [year] => 2012
                [month] => 2
                [post_type] => post
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        [122] => stdClass Object
            (
                [slug] => design
                [ID] => 1128
                [post_name] => keine-panik-auf-der-titanic
                [post_title] => Keine Panik auf der Titanic ...
                [post_author] => 2
                [post_date] => 2011-08-24 15:54:49
                [year] => 2011
                [month] => 8
                [post_type] => post
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        [123] => stdClass Object
            (
                [slug] => design
                [ID] => 1082
                [post_name] => coffein-and-theobromine
                [post_title] => Coffein and Theobromine
                [post_author] => 2
                [post_date] => 2011-07-23 11:37:52
                [year] => 2011
                [month] => 7
                [post_type] => post
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        [124] => stdClass Object
            (
                [slug] => design
                [ID] => 1080
                [post_name] => generalized-polygons
                [post_title] => Generalized Polygons
                [post_author] => 2
                [post_date] => 2011-07-23 11:37:06
                [year] => 2011
                [month] => 7
                [post_type] => post
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        [125] => stdClass Object
            (
                [slug] => design
                [ID] => 1046
                [post_name] => choose-your-weapon
                [post_title] => Choose your Weapon
                [post_author] => 2
                [post_date] => 2011-07-22 20:21:37
                [year] => 2011
                [month] => 7
                [post_type] => post
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        [126] => stdClass Object
            (
                [slug] => design
                [ID] => 1103
                [post_name] => unterbezahlt
                [post_title] => Unterbezahlt
                [post_author] => 2
                [post_date] => 2011-05-24 14:13:36
                [year] => 2011
                [month] => 5
                [post_type] => post
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        [127] => stdClass Object
            (
                [slug] => design
                [ID] => 1044
                [post_name] => rock-paper-scissors-lizard-spock
                [post_title] => Rock-Paper-Scissors-Lizard-Spock
                [post_author] => 2
                [post_date] => 2011-05-22 20:20:44
                [year] => 2011
                [month] => 5
                [post_type] => post
            )
    
        [128] => stdClass Object
            (
                [slug] => design
                [ID] => 1148
                [post_name] => plexiglas-t-shirt
                [post_title] => Plexiglas-T-Shirt
                [post_author] => 2
                [post_date] => 2011-04-24 16:51:30
                [year] => 2011
                [month] => 4
                [post_type] => post
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        [129] => stdClass Object
            (
                [slug] => design
                [ID] => 1078
                [post_name] => coxeter-and-dynkin-diagrams
                [post_title] => Coxeter and Dynkin Diagrams
                [post_author] => 2
                [post_date] => 2011-04-23 11:36:11
                [year] => 2011
                [month] => 4
                [post_type] => post
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        [130] => stdClass Object
            (
                [slug] => design
                [ID] => 753
                [post_name] => polymake-logo
                [post_title] => polymake-Logo
                [post_author] => 2
                [post_date] => 2011-03-28 00:21:16
                [year] => 2011
                [month] => 3
                [post_type] => post
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        [131] => stdClass Object
            (
                [slug] => design
                [ID] => 1088
                [post_name] => true-story
                [post_title] => True Story
                [post_author] => 2
                [post_date] => 2011-02-23 12:56:31
                [year] => 2011
                [month] => 2
                [post_type] => post
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        [132] => stdClass Object
            (
                [slug] => design
                [ID] => 1040
                [post_name] => t-shirt-design-im-not-crazy
                [post_title] => T-Shirt-Design: I'm not crazy ...
                [post_author] => 2
                [post_date] => 2011-02-22 20:16:23
                [year] => 2011
                [month] => 2
                [post_type] => post
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        [133] => stdClass Object
            (
                [slug] => design
                [ID] => 764
                [post_name] => adm-logo
                [post_title] => ADM-Logo
                [post_author] => 2
                [post_date] => 2011-01-28 00:24:39
                [year] => 2011
                [month] => 1
                [post_type] => post
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        [134] => stdClass Object
            (
                [slug] => diy
                [ID] => 739
                [post_name] => stephan-mag-panzer
                [post_title] => Stephan mag Panzer
                [post_author] => 2
                [post_date] => 2011-01-28 00:09:47
                [year] => 2011
                [month] => 1
                [post_type] => post
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        [135] => stdClass Object
            (
                [slug] => diy
                [ID] => 736
                [post_name] => drink
                [post_title] => Drink
                [post_author] => 2
                [post_date] => 2011-01-28 00:08:50
                [year] => 2011
                [month] => 1
                [post_type] => post
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        [136] => stdClass Object
            (
                [slug] => diy
                [ID] => 730
                [post_name] => three-hearts
                [post_title] => Three Hearts
                [post_author] => 2
                [post_date] => 2011-01-28 00:04:10
                [year] => 2011
                [month] => 1
                [post_type] => post
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        [137] => stdClass Object
            (
                [slug] => diy
                [ID] => 727
                [post_name] => blurred-checks
                [post_title] => Blurred Checks
                [post_author] => 2
                [post_date] => 2011-01-28 00:02:18
                [year] => 2011
                [month] => 1
                [post_type] => post
            )
    
        [138] => stdClass Object
            (
                [slug] => diy
                [ID] => 721
                [post_name] => schwarz-weiss-rot
                [post_title] => Schwarz-Weiß-Rot
                [post_author] => 2
                [post_date] => 2011-01-27 23:53:37
                [year] => 2011
                [month] => 1
                [post_type] => post
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        [139] => stdClass Object
            (
                [slug] => diy
                [ID] => 718
                [post_name] => trianglar
                [post_title] => Trianglar
                [post_author] => 2
                [post_date] => 2011-01-27 23:44:53
                [year] => 2011
                [month] => 1
                [post_type] => post
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        [140] => stdClass Object
            (
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                [post_title] => Truck-Collection
                [post_author] => 2
                [post_date] => 2010-12-15 00:14:44
                [year] => 2010
                [month] => 12
                [post_type] => post
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        [141] => stdClass Object
            (
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                [post_name] => google-telephone-interview-rant
                [post_title] => Google Telephone Interview Rant
                [post_author] => 1
                [post_date] => 2010-10-27 22:30:02
                [year] => 2010
                [month] => 10
                [post_type] => post
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        [142] => stdClass Object
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                [post_name] => hello-world
                [post_title] => Getting started
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                [post_date] => 2010-10-02 11:12:43
                [year] => 2010
                [month] => 10
                [post_type] => post
            )
    
    )
    
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