I finally got around to making the pentakis dodecahedron from the instructions in Math Craft admin Cory Poole's blog post. It's not tightened/straightened up yet because I just noticed that I have two black and white and two blue and green compound modules next to each other (but no purple and pink modules next to each other—to the math experts, this is a parity thing, as you can only have even numbers of modules paired up next to each other).
I am still pretty happy with it, but after posting, it is going to be deconstructed to get the colours right. I might even abandon the multi-colour aspect and go for just two colours, as I think it might be more striking.
One other thing I tried for the first time was small sonobe. I was enchanted by Rachel's tiny sonobe models here so I decided I would make the pentakis from pretty small squares of paper. This model is made from squares 5cm wide on each side. To get an idea of scale, here is the model in my hand:
Here is a cube made from the same size sonobe (the cubes will have to become Christmas tree decorations):
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22 Comments
Looks great! I need to play with smaller squares... I'm not sure on the parity thing but it sounds reasonable. I always decide that the hardest problems to think about are the ones that involve combinitorics...they make my head hurt. :) Hopefully someone else can help you out.
Just tried to put it together again and have a mis-match at the end. grrr. I might leave it this time as it is getting pretty tired and it might rip if I dismantle again
Just went for a wander around the net and I cannot see any pentakis dd's that have a regular rotation of colour - they nearly all have loads of higgledy-piggledy colours or just two or three with lots of repeats. I try a twelve colour design based on the faces of the base dodecahedron
Seems like there has to be some information on a vertex coloring of a dodecahedron. I'll search sometime because now I'm curious.
Check this out from George Hart Am I incorrect in assuming you should color this like the faces of an Icosahedron (I know that you don't really have triangular faces...but it seems like the underlying symmetry is the same.) So basically it seems like you could end up coloring it like the 5 intersecting tetrahedra again. But maybe I'm missing something.
Oh. I get it ...I forgot how these units connected...I was thinking that each double unit was just it's own color...hmmm....
wow interesting article from hart... i never thought about the mathematical application of coloring.
Does anyone know if there's a free program for Macs that lets you view Hart's .wrl files? Or just a working browser plugin? I tried Instant Player and FreeWRL with no luck.
I think .wrl files are just vrml files. So you might go searching for mac versions of a vrml viewer or browser plugin. I'm not a mac guy so that's all I've got.
Yeah, I tried those two above and Cortona is no longer available. Darn. And I can't figure out how to install orbisnap (if that even works). Oh well.
I was thinking more of colouring basis the 30 edges of the dodecahedron rather than the twenty faces of the icosahedron. The pentakis of anything can be thought of as putting a spike where an edge should be - if I am right then I can colour it so that half of every "face" of the dodecahedron is one colour. Every compound would be different so I would have to make them up as I went. Will read the George Hart page - but his maths is just so far beyond mine that my head spins.
beautiful. love the scale you chose.
I'm bummed because I can't figure out how to make one... though I haven't given it my top effort just yet. I've been working on a quilt, which i plan on finishing this week... once that's done, I'm going to go hardcore origami up until the holidays.
"hardcore origami" definitely. I have had horrible day so far - so I will spend an hour or so this evening with the music at 11 and with some folding. I will take some snaps - and if it works out I will blog them
i hear you. folding origami is calming.
Btw Rachel I am in the middle of building a Menger Sponge origami I will post it to the corkboard.
Awesome! Are you using sonobe units (like in Rachel's post) or something else?
Sonobe units. I know of no other way except this and the buisines card one.
Cool. You should explain a little bit about how to do it when you post it up. A small (or big) tutorial would be awesome. (I understand that you're busy though.)
Yea, I will. The only big part that you have to learn is folding the sonobe units, the rest you can do yourself. all you have to do is connect the units. I am making it out of yellow and green post it notes.
@ cerek (menger sponge) yay!! can't wait to see it.
@cerek Cool. It would mainly be nice to see how the units connect. The post it notes idea is cool. I've thought about that before. How much does the stickiness affect the folding?
Really, it doesn't at all when connecting the units. It only affects you a tiny bit when folding the units. Right now, I am out of origami paper so I just use post-its (:
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