The Origami Forum

i am OBssessed with the stella octangula shape i would really lie to make one froma single shet of paper..i mean it HAS to be possible. I do not think i'll be able to get montroll's book uhmm origami polyhedra constellations or something....and uhmm...there HAS to be a way to creat this shape that is sturdy and elegant.....

in the process following my obsesssion has led to dividing the paper into 6'ths on one side, and 7'ths on the other, and connecting the corners of the resulting rectagles creating a grid of equilateral triangles. and that is the bases of this...18 equilateral triangles forming 6 tetrahedronal points... and that gives you 2 inverselly intersecting tetrahedron.

the keplar star in the origami omnius is one, but is a modular peice...and montroll has a single sheet one but i dont think i'll be getting that book... and besides i wanna kinda create one, with the help of someone too

here is another modular
http://www.ceciliacotton.ca/archives/00000185.htm


any tips?

Yes, always enable BBCode in your posts, especially if you use it!!!

That is a coincidence-I have been turning over the idea in my head, too. A stella octangula (or stellated octahedron) is interesting, because it is not convex. That is, not all of its surfaces approximate an outward curve; some "curve" inward. That means that it is not just a problem of reverse-folds hiding paper to produce the surfaces.

If that is confusing, try this: there are points (6 of them) on a stella octangula where 8 equilateral triangles come together at a point. 60 degrees x 8=480 degrees. That is more than 360, which is the number of degrees in a circle, or around any point on a flat surface. So you need to "add" paper around that point. By add I mean hide paper inside the model in a way that brings together 8 equilateral triangular faces. It should be possible to hide a star-shaped (4-pointed) section of paper to bring together 4 groups of 2 equilateral triangles each. Those compounds of 8 facets each will then have to be brought together with each other to form the final shape.

I haven't gotten much farther than that, but the other thing that would be difficult is locking it together at the end...

Before start working on it on the wrong way, keep in mind that the stella octangula you are talking about


It isn't a stellated tetrahedron, but a stellated octaedron

That is a solid figure like that:

with an equilateral piramyd on each face.

By the way, the eight top point of each piramyd marks the vertex of a regular cube

hmm very interesting.....

i have found this http://www.korthalsaltes.com/stella_octangula.htm

and tried to apply it to a grid on equilateral triangles. now, trying to collapse the model does not work because the paper will not allow itself to seperate certain parts....

ok so... the learning that has occured is that the basic "module" for three equilateral triangles forming a point (with an open bottom) is three equilateral triangle next to each other.. however i have not been able to translate the lang theory of modules..or tiles or whatever, into a 3-d shape.

there must be a way to figure out how to lay the (i said 6 points in the first post, actually it is 8 points) 8 "tetrahedron" "modules" out.

This is so close, but so far away....there needs to be more paper between the top two flaps of the linked picture, because those two points actually dont end up touching, they need more space between them. the point from the bottom of the "net" comes up in between them...

hmm so, is there a way to make the lang tile theory incorperate into a 3-d flap?

Also...there need to be pockets and flaps to concrete the closing of the model...ive actally been thinking of maybe doing some sort of "wrapping" the paper around itself to create the shape....kinda like a lucky star but complexly different. anyway..... there must be some mathmatical or logical way to figure this out

ps. thanks anna...i had all those options turned off for some weird reason..heh, i guess trying to make life difficult for myself as usual the preview button is out friend

I'm not clear which is which, but here are a few references:

1. Lang: Complete Book of Origami, p. 58 Stellated Cubocta
2. Kasahara: Origami Omnibus, p. 214 Kepler's Star
(Intersecting Tetrahedra - modular)
(Also see Stellate Octahedron on p. 242 - modular)
3. Crawford, Patricia: Stellate Octahedron, The Origamian - Vol.12 #2,3,4
4. Best, Kim, Stellated Octahedron, OUSA Convention Book 1998, p. 34
5. Gross: Art of Origami, Stellated Octahedron by Sam Ciulla, p. 34
6. Thoki: CubeOctahedron http://erikdemaine.org/thok/cubeocta.html
7. Montroll: A Plethora of Polyhedra in Origami
8. MOntroll: A Constellation of Origami Polyhedra
9. http://www.instructables.com/id/Single- ... ctahedron/
10. Look up "stellated octahedron" on Google images...

HTH,
Hank Simon

That instructibles model looks decent, although it uses right isosceles triangular faces instead of equilateral triangular faces. Maybe the concept could be adapted, though.

I cross-posted the question on the Origami-List, and no one had info on the Crawford model.

You CAN buy "A Constellation of Origami Polyhedra" by John Montroll from Amazon for about $10 - $12.


Best, Kim: Stellated Octahedron, OUSA Convention Book 1998, p. 34
This is 1 sheet.

But I did get a little more info:
[Anne LaVin]
http://mathworld.wolfram.com/StellaOctangula.html
This model appears to be an octahedron with somewhat squat
triangular-pyramidal points - each point's geometry is made from
collapsing the diagonal and only one of the "bookfold" creases of a
waterbomb base so you're left with a pyramid. Each face is a 1-1-rt(2)
triangle, in other words.

To the best of my understanding, neither Sam Ciulla's nor Kim Best's
models are, actually, a "Stellated Octahedron" - the only proper
stellation of the ocathedron is named the "Stella Octangula."

Which takes nothing away from the models, they just should be called
something else, mathematically-speaking. ("Octahedron with spike-ish
bits sticking out," however, fails to roll off the tongue.

But - mathworld again to the rescue - have just discovered that the
proper word is "cumulation". Thus, math-speaking. those two models are
"Cumulated Octahedrons." (http://mathworld.wolfram.com/Cumulation.html,
where there's even an image of one.)

[Sy Chen]
John Montroll has both Stellated Octahedron (45-45-90 triangle) and
Stella Octangula (60-60-60 triangle) diagrammed in his book - A
Constellation of Origami Polyhedra. If you read the diagram carefully,
Both of them can be collapsed from regular cube. i.e. You can fold a
traditional waterbomb with extra pre-creases in the beginning to start
with. The final collapse can give you either of Stellated Octahedron
and Stella Octangula depending on your pre-crease pattern.

Actually Sam Ciulla designed a stellated Octahedron from regular
waterbomb. The approach is surprising simple and elegant. The diagram
can be found in Gay M. Gross' book - The Art of Origami.


Kim Best's model is a Stellated Octahedon. Although the shape is the
same. Ciulla's approach is my personal preference.

As for Crawford's Stella Octangula, I believe it is from a hexagon.

- Hank Simon

I was not aware that there was a difference between stellated octahedrons and stella octanulas (stellas octangula?). Regardless, you shouldn't be able to do either just by adding creases to a cube, for the reason I described in my previous post.

I got most of the way through designing one a few months ago, although I never made a final version. I used a pattern similar to Roberto Gretter's Turtle (http://ditelo.itc.it/people/gretter/origami.html)

As Jon speculated, closing it on the other end is the most difficult part. The rest of the model isn't very hard once you get the basic pattern down.

oh man, that is some good information. so.. the stella octangula is realated to a cube....i must do some experiments with this to try to get this to work....souds like it would be nice... i tried the one from instructables, and i was very pleased with its result..however it was not the 60-60-60 triangles i was hoping for.

thank you all for taking an interest in this subject

amazon says you ca get art of origami for like 2 dollars or less even.... what else does this book have? i havent seen any reviews on it, like from gilad or anything.

Try Google books...

Search Google for "A Constellation of Origami Polyhedra" WITH the quotes, and it should come up around the fourth item...

You can see the Table of Contents and about 15 - 20 pages...

http://books.google.com/books?id=fiL9Kb ... lt#PPP1,M1

- Hank SImon

I too am a fan of stella and any polyhedra modular units, it you like the sonobe module and the models you can make with it, i encourgae you to pick up Tomoko Fuse's book
Unit Origami: Multidimensional Transformations
http://www.amazon.com/Unit-Origami-Mult ... gy_b_img_c

you can learn many other modulars, i have been using the Sonobe module to create triangle cupolas and forming larger polyhedra with those, the open frame unit is also one of my favorites.

http://public.fotki.com/AddieGoodvibes/ ... creations/
password = bushido

hmm, we were talking about making one out of one sheet though. It's a lot harder

I could be wrong here, but if you were to make a modular version, see where paper overlaps and then connect them, removeing the overlaps? Only problem would be making it in a good shape of paper to start with.
it could have a large amount of "wasted" paper. though it would be less then in the modular version.