Origami Platonic Solids

The Platonic Solids

Also known as the "regular convex polyhedra", these five are the only forms that are convex (ie: not hollow and no "dents" in them) and with every face having the same shape ("regular"). Hoorays!

In order of complexity, these are:

Tetrahedron	4	equilateral triangles
Hexahedron / Cube	6	squares
Octahedron	8	equilateral triangles
Dodecahedron	12	regular pentagons
Icosahedron	20	equilateral triangles

Those who play games like Dungeons & Dragons are probably already familiar with these.

Johannes Kepler liked to study these!

Johannes Kepler (1571-1630), best known for his three laws of planetary motion, was one of the most outstanding mathematicians of his day. In addition to his astronomical accomplishments, he systematized and extended all that was known about polyhedra in his time. While previous artist/geometers discovered particular polyhedra, he took a more mathematical approach: he defined classes of polyhedra, discovered the members of the class, and proved that his set was complete.

- from http://www.georgehart.com/virtual-polyhedra/kepler.html

Kepler also believed these polyhedra were associated with the elements:

Tetrahedron	Fire	It has the "shape" of fire; and there's also the fire tetrahedron teaching tool, which is neat!
Hexahedron / Cube	Earth	It's very stable.
Octahedron	Air	If you hold this model lightly by the two farthest corners, and then blow, it will spin like a top!
Dodecahedron	the Cosmos	It has twelve faces, and there are the twelve constellations (in astrology, zodiac).
Icosahedron	Water	It has a similar property of that octahedron, like it moves easily or wants to move, the way fluids do.

Origami

So I finally got around to making origami models of each! These are modular skeletons:

Tetrahedron	6 units	Francis Ow's 120-degree module
Hexahedron / Cube	12	Bennett Arnstein's Variation of Lewis Simon's Decoration Box modules
Octahedron	6	Lewis Simon's Gyroscope module
Dodecahedron	30	Lewis Simon's / Bob Neale's 108-degree module
Icosahedron	60	Francis Ow's 120-degree module

...more later?
--Charlie

Origami etc

Origami

Started on another fish tank origami display. This time, I'm using a fish tank my mom doesn't want, so there'll be no fear of her taking it apart again!

Picked up Origami Design Secrets: Mathematical Methods for an Ancient Art by Robert J. Lang.

It's absolutely wonderful. It's not just a "folding" book with only instructions and minimal literature. It goes into how models have been designed and gives tips. The first or biggest tip is this: modify an existing model; don't expect to create something totally original at first. I like that. He writes something to the effect of "no design is sacred", meaning it's totally open for modification or interpretation.

The only thing I don't like is my inability to accurately reproduce those models--I guess "difficult" would be the word, but my biggest problem is getting the proportions just right. For example:

I'm instructed to fold the paper in half and just make a pinch mark at the halfway point. Then, halve that half and pinch again at the one quarter mark. Then, make a crease from the half-way mark, and bring the far corner of the paper to the one-quarter mark.

Problems:
- the pinch marks are nearly invisible on the white side of the paper
- the pinch marks are rather thick, increasing error
- some paper doesn't like pinch-marks: it'll resist the fold unless it's creased all the way.

Ah well.


New origami pieces added to my deviantArt gallery:

Writing

I'm starting a writing exchange with Kevin. So far, I've sent him a link to Stipper and Jo, and he's sent me a poem about dying in a car crash.

Hehe.

He seems to have a morbid fascination with car crashes--or, I dunno, maybe. His film group's name references it; and he's sent in two submissions for his university's literature journal about car crashes. He said the other day that maybe this is why he hasn't got his driving license yet.

Anyway. This poem he sent is...yeah, morbid--unexpectedly morbid. The end cuts off like in Margaret Laurence's Stone Angel.


Kevin

Went to the library with Kevin on Wednesday. We're kinda geeky, but I don't at all mind. He checked out books on David Lynch (he's just finished Twin Peaks) and some DVDs. I took out Origami Design Secrets: Mathematical Methods for an Ancient Art by Robert Lang and The Origami Bible by Nick Robinson.

We talked about English, about literature, about language and communication. We took the same bus back, and I recited part of I Could Be A Poet by Taylor Mali, and some of Stipper and Jo by me.

Stipper and Jo is one of those poems that has to be read aloud for the full effect. When I wrote it, I had in mind a quick pace, and a British accent. I kinda want to perform it one day.

Anyway, so I was reciting poetry on the bus; and I was drinking coffee (actually, a "Black Cherry Pie", which is hot chocolate, espresso and black cherry syrup--delicious!), so I spoke rather loudly and excitedly. I just about missed my stop because of it. A lady happened to get off at the same stop, and she turned to me and said, "That coffee sure got you going, didn't it!"


As I was walking, I thought about how I fit in the world. Sure, at home or at work, I can be ME with very little thought about what people think; but on the street, who am I?

I thought about the way Kevin might see me. When I got my hair cut this short, he was the first one to see it, and he said nothing. None of that, "Hey, you got your hair cut, it looks nice" bullcrap. And I loved that!

I don't know why he said nothing; maybe he's never said anything about girls' hair before? I don't know, but I don't really care, either. I'm starting to see that honesty--"earnest"-ness in him.

Argh, and this is all after realizing/deciding we wouldn't work as a couple. I guess I still stand by that, but I'm freeing up the type/s of relationship we could have.

"Fluid" is a word I'm starting to use to describe myself--to myself, at least. I change, I flow smoothly, I fill empty spaces, my boundaries are ever changing and I am not restricted to one shape or size--ideally, at least.

So, again, I wonder how he sees me. Probably he sees me as that passionate artist sort, which is nice. I wouldn't mind that.


My Faults

I really like myself. I'm very comfortable with who I am, and not...willing / eager to change, so I can be pretty unmotivated / lazy.

I love attention; I'm pretty self-centred or self-absorbed and sometimes I have to stop and remind myself that not everyone is as "open" as I am, so I have to ask them very specific questions in conversation. I'm working on this, though.

I'm often late. Working on it!


[ post abandoned... ]

CAMERA at last!

The camera finally arrived, which means I can take pictures again! Further, I can upload pics of the Origami polyhedra I constructed! Here we go!



Left to right:
30-mod (sonobe) stellated icosahedron;
12-mod (sonobe) stellated octahedron;
12-mod (sonobe) cube.


Left to right:
12-mod decoration box; assembled into a 14-box ring;
6-mod (gyroscope) truncated gyroscope (?).


Finally: 6-mod flower-box. It changes from a box to a flower! Amazing!


...Will update more later, maybe.
--Charissa

Quick Update

Origami

For my birthday, I received an Origam gift box and extra book from Mark! OMG! The gift box has printed paper (strange and elegant designs that remind me of wallpaper), gold and silver foil paper, a protractor, two 'bone' crease tools (one for making sharp creases, the other for "drawing" the crease patterns), a square board with grid and markings on it, and an origami instruction book. I'm only a little irritated that both books contain mostly diagrams that are reliant on cutting paper.

This is mostly an announcement that, as soon as I get my camera, I'll be posting picture of both the modular origami polyhedra and the new models--animals and flat geometric patterns. Man, I can't wait to get that camera!!


Teaching Math

I've been in correspondence with one of the students who had questions about exponents/roots, and after the two weeks between classes when I was helping her with that, she wrote back to say I'm a good explainer! That totally made my day!

We started conic sections on Saturday with the Circle and Ellipse. At the end of class, the teacher wrote this on the board:

"Next week: line, parabola and hyperbola."

The students had mostly never heard of hyperbola, and some never heard of parabola. The teacher said to look it up on the Internet, and I wanted to jump up and say, "MATHWORLD DOT WOLFRAM!!" but of course, that would have been inappropriate, so I didn't. Sigh.


Film Festival

One of my friends has a film in a Canadian film festival, and his film made it as far as a public showing! I'm so excited! I'm going to the showing, hopefully with a friend who is/was a major artistic-film-maker-type-person. In truth, I wonder if she'll like my friend's film, but I invited her mostly for the other films. Heh.


Army

My unit did a field exercise this past weekend. They slept outside with little form of heating for two nights. Yowza! I went on the last day to help with breakfast and tear-down. Man, I suck at moving things. I definitely need to work out. But with the army, I get a personal trainer and access to the gyms, so I'll have to make use of that. Sheesh, though, I wish I had more free time...


Art

I'm donating Boobfest III to the queer student group at the university I used to go to. At least, I'm donating a print--and I think I'll take it back at the end of the school year.

Also, that student group is planning on booking a small art gallery in one of the centres at the university--there's this glass room beside a major traffic junction and across from a Tim Horton's / food court, I think, which is totally a great place to put an art gallery.

If we end up booking it, I'll totally submit: my nude pieces; the Origami I'm proud of (goldfish in the bowl!!), including an enclosed chain of connected coloured boxes that are ordered to make a rainbow (sort of; I'm missing a real *purple* but I have this dull mauve thing); and any other artwork I deem public-worthy--which is not much, so I'll have to get busy making more, dammit! Mmm, I'm excited!


...Will update this entry with links and text formatting later.
--Charissa

Novemberance!

As a kid, I used to call today "Novemberance Day" and even wrote a terrible poem about it, once. I dunno, I never had a particular attachment to Remembrance Day. In school, one of my good friends, Diane, had/lost family in the World War/s, I can't quite recall.

But as a member of the Canadian Forces, I was at one of the many Remembrance Day ceremonies across the city. Of course, I have no training as of yet, so I was, at most, a spectator standing with some higher-ranked personnel who told us untrained Privates when to stand at attention, remove our headdress and so-on.

A few things were prominent today...

I know it shouldn't be funny--especially not today--but it can be rather hilarious when you actually see soldiers--mostly Cadets--pass out while standing on the parade ground. I was told that it's quite common, especially with the Cadets, for soldiers to get dizzy and pass out from standing for about two hours--especially the Cadets, who are often so nervous that they "thunder"; fall, stiff as a board, flat on their faces. One guy from our unit even fell on his face; and then began crawling about as though uncertain of where he was. I was told he lost a contact lens in the process.

My "boss" is disgusting. Really, she is. She's short, skinny, butch, loud, irritable, vulgar, and disgustingly, disgustingly hetero. I really did not want to hear her talk about condoms nor "sword-fighting" in her mouth. She reminds me of a girl I knew in high-school, except she's an adult. I want to believe that she's just disgusting when she's in uniform, it's her coping mechanism or something, but she makes me want to vomit--I can't believe she's a soldier! Does she have dignity? IT SURE DOES NOT SEEM SO!

I do not have to adopt a new lifestyle. Here is (sort-of) a summary of my thinking:

- I'm in the Army, hoorays! I'll have discipline!

- Oh, I'd better watch and learn from observation!

- Gee, this is a lifestyle thing!

- I'd better bring Army elements into my Civi lifestyle!

- Son-of-a-bitch, I'm getting a soldier's mouth!

- Hey, my "co-worker" has morals and refuses to profane!

- That is freaking awesome!

- I'm not going to profane! Nor drink--the way they do, at least.

- I don't have to be like anyone else! I'm special!

So, hoorays!

Remembrance Day is important! This I already knew! It just feels... more ceremonial--of course--now that I'm in the CF.

The Remembrance Day ceremony was Christian! Some of our speakers were very... "We are fighting Evil!" which made me a little uncomfortable. We fight Evil, yes, but it is not... We don't... We aren't to be "Holy Warriors", I think. I think we should never be "Holy Warriors". ... Sheesh, this is difficult to put into accurate words!!


In other news...

I found out something interesting the other day. I'm not yet going to say what, because it's not my story to tell; but it made me both excited and... Clingy. I mean, it's a bad thing to be excited over this. HONESTLY.

Also, at the Maths school, we gave out a rather fun-looking assignment. I do and don't look forward to marking these! They're all long-answer involving Trig Identities. Sigh. While it'll be exciting, it'll also be messy and headache-inducing, I think. Woots!

Also, I took out a book on Modular Origami from the library! I've already made a stellated icosahedron. Woots! I think, after I finish making some of the models in this book, I'll move onto this project! Bwahah!


That's all for now. I might update later with fun trig stuff.
--Charissa