thing-a-week 8: flexagons + quick tutorial

I wanted to do something with the grocery bags that are piling up in my place, so I made some flexagons.

Wikipedia says that these are "models", though I don't know what they're models of. I just think of them as paper toys that change faces when you fold them a certain way.

Here's my flexagon with abstract, bacteria- and coral-inspired designs:

Face 1…

…folds back to show…

…face 2, which…

…folds back to show…

…face 3, which, …

…when folded back…

…brings face 1 back again.

I used pencil and markers for the lines and colored pencils for the fills.

Originally, I wanted to do a "town and country" theme, so I came up with the flexagon below. But, I didn't color it all the way, because I wasn't happy with the way the crayon looked on brown paper.

Skyscrapers for face 1…

…fold in to show…

…townhouses on face 2, which…

…folds in to show…

…a tiny farm planet on face 3 (which folds in to show face 1 again).

Now, flexagons are pretty easy to make. The ones in this post are actually called trihexaflexagons, because there are three faces. But, you can make flexagons that show even more faces; I've seen dodecaflexagons.

Flexagon.net is a pretty good place to start. You can either download a template from there and print it, or draw the templates manually like I did.

If you do make a template by hand, I suggest using a protractor to make sure that each triangle is equilateral. I also had to use the Pythagorean theorem to figure out the height of each triangle.

If you're impatient to give this a try but don't have a printer and don't want to use math (boo!) my triangles had these dimensions:

length of side = 3 cm
height = 2.6 cm

For a trihexaflexagon, draw the triangles in two lines like so: (PDF). Follow the folding instructions there as well. I wrote the guide letters really tiny in the corners and then erased them after the glue dried.

Once you're ready to design, decide whether your flexagon will fold in or fold back:

Folding in: Face 1 goes inside; face 2 appears outside.

Folding back: Face 1 goes outside; face 2 appears inside.

If you fold one face in and one back, at least one face will come up inverted (of course, that could be just what you want).

UPDATE (022613): After going home and checking the flexagons, I realized that what I really wanted to advise you against was designing one face, flipping it over, designing that, and then folding in/back and designing the third face. That's what gets you an inverted flexagon face. Fold in or back, it doesn't matter, as long as you fold before you design.

Design each face in the order you want. The design for each face is up to you, of course. Last year, I gave a flexagon instead of a birthday card. I also read about a teacher who taught his students to make flashcards out of flexagons, with each face featuring a different word and definition.

Let me know if this post is useful to you or if I could clear it up somehow.

So far, I've made only trihexaflexagons. I tried a tetrahexaflexagon once but couldn't figure out how to get the fourth face to appear. I guess that's something for another day.

Who is the hero?

I dreamt that we could be in movies. We'd buy tickets and popcorn, enter the theater, and then be in the movie.

I was in a movie with four other friends (Martin was there), and the movie started out as a parody of epic movies but quickly became the real thing. We were a band of warriors helping a prince complete his quest, and I got to be the tough girl.

There were five monsters we had to kill. The first was in a prison, where the soldiers of the prince's own kingdom wouldn't let us go. They battled us and brought out a balrog-type monster to help them once the good red nuns and red knights were out of sight.

The second monster was waiting underneath an overhang, near the opening of a chamber where I think there was treasure. As we entered, we passed a screeching bird with the head of a woman on its shoulders. It looked harmless, but I had the feeling it was the monster. Sure enough, it attacked once we had all entered that dark and narrow chamber.

The harpy became another woman in armor, and she was beautiful (her head actually resembled the Sphinx in Subnormality) but still out to kill us. She did battle mainly with the prince, but it was i who found her weak spot, under her arm, and there I plunged my sword to the hilt.*

She looked at me a moment as though impressed, like I'd passed some sort of test, and then she stumbled back out of the chamber and (I think) she died.

We didn't take any treasure and almost immediately followed the harpy. In the bird's place on the natural stone table was an old woman. We had to walk past her in single file to return to the road. I led the way because I knew she was the harpy, and sure enough, she pulled out a shiny new butcher's knife.

I blocked her attack with my sword, and the others slipped past us to retrun to the road. The old woman didn't try to kill me, only pushed with her cleaver so she could lean close. She hissed at me something about fighting and love. She made me repeat it to her and, satisfied, she got off the stone table and joined us on the road.

(I'm kicking myself right now because I can't remember what she said. But I suppose my subconscious does, so I'll be okay.)

The harpy walked with us only a short way. Then she quietly took the other path when we reached a fork in the road.

Then we left the movie theater, happy with our achievement and eager to return for the other three monsters, but shaking inside form how actually life-threatening it was. Martin, tired, went to the concession stand for a large soda. Lemon-lime.

After that, I'm not sure if we went home and started a new movie there or went back inside the cinema.

It was supposed to be a children's movie with a similar theme. We were helping five toys prepare for an epic quest. As we were about to leave, the youngest toy, a little yellow potato-like ball named Weegle, disappeared into the house to get his favorite hats. I took the pirate hat to give to a tough little Lego girl, only the hat turned into a dead Lego pirate mummy that she sort of had to carry piggyback.

We set off on our quest--it wasn't the toys anymore, but us, and we rode in our choice of cool superhero vehicle. I had kind of a hog bike.

We ran into a bunch of black bikers in the desert, and they challenged us to a race (a deadly one, of course). They brought out their big cars and bikes, and something was wrong with the vehicles of the guys on our side. They wouldn't start, or they wouldn't go fast enough. I decided to try anyway and took off on my hog.

There was a slim chance I'd win, but I was having fun. Just as I started to speed up, though, I suddenly had no bike. I was walking down the white track, and there was a tall, black-as-night man walking with me. His bearing was noble, even if he was completely naked. Maybe because he was naked. We walked at a normal pace.

When we got to the cluster of bikers, they parted for us, and I knew that the black man was a prince and a god, maybe a lesser god, but still a god, and I was safe.

But not for long. The biker men couldn't do anything, but an older woman came out of a hut by the track and began performing a ritual that would capture me and the god. There were purple chalk circles on the track, and I knew if we both stepped in them, we were lost. The god walked on as though nothing was happening, even though I knew he knew perfectly well what was happening. It was me protecting him now. He got weaker with every spell, it seemed.

i did things to break the circles, I really had no idea, just did what came to mind. Picked up the cloth edges of the track to shake it and scatter the chalk. Stepped on or kicked purple flowers. At one point, I thought to mix dust into the chalk, and the elder woman wailed.

She got more desperate now. She cried out that she could give me shelter from the rain. For some reason, this made me cry. Scared, I ran to the god, and I curled up at his feet, and he covered me with his body and said the only thing he ever sad that whole walk, "Take shelter in the rain."

When the woman's magic passed over us, we continued on our walk along the track. I was weak now, but the god was weaker still and leaning on me for support. The elder woman, still following, must have been really desperate. "You must be hungry!" she cried. 'I have siopao. Do you want siomai rice?" Because this was really ridiculous, I gave her my snottiest "No!"

She followed us to the end, right up to the edge of our homebase. Up to this point, the men of either side had done nothing and had simply watched our progress along the track, because this was the way. Once the god and I stepped over the boundary line (really, a low cement line sticking out of the dirt) and onto our own damp soil, our warriors closed ranks around us and kept the woman out.

She continued to make her pleas, but I ignored her and lifted the god up against a crumbling rock the size and shape of a pyramid brick, or a tomb. A young man came to help and began wrapping the god up in fresh linen bandages. By then he was rotting and struggling to breathe; he would be dead before the young man finished. But it was okay, because we were with our own people.

The men were chanting something, three alien words, which were still booming in my head when I woke up.

In that fading phase where you can still feel the dream even though you're awake, I returned to the tomb rock at night. The god-prince was standing there in his bandages and a tricorner hat. I somehow felt that he was one of the monsters, but also that this part of the quest was past. He embraced me and then kissed me, and then the next moment it was morning and I had to take his body to the sea.

Later in the morning, while getting ready for work, I realized that it was actually the second time I've walked with this figure in my dreams and escaped those purple circles, but it wasn't such an elaborate, ritualistic even the first time, and I didn't see all this bandaging stuff.

Interpretations, anyone?

--
*This is only the second time I've ever dreamt that a strike had the force and effect I'd intended. The first was when I kicked that gangster in the balls. But that's another dream.

Toy Stories

We caught "Toy Story 3" last Friday, and while I enjoyed it, I have to say that I still like the previous two movies better. I think it's the months of hype that pushed my expectations so high. I should sit down and watch it again when it all dies down--that's always how I best enjoyed the previous two movies, anyway: on the living room floor with my brothers, surrounded by their toys.

The movie did get me thinking about my own toys, though; the ones that are still stashed somewhere in my room at home and waiting for me to have kids so they can come out again. This is a list of the ones that stand out in my memory. (I wish I had pictures, but I'm not home right now to take them.)

Faded pink teddy bear. I stubbornly held on to this one, not because I actually had any strong attachment to it--I didn't even play with it that much--but because something in the back of my mind told me, "You have to have something that you've had since nursery school. All the life stories you've heard have someone holding onto something they've had since nursery school."

Sparkly purple teddy bear. Kind of itchy and not even that soft. I remember this because it was one of the first toys my parents got me when we'd first moved to the States. We were still living in the San Joaquin Hotel and our stuff hadn't arrived yet, so my brother and I picked out a few toys from the Salvation Army.

Big box of Lego. My brother Mikko and I shared this toy, also since our San Joaquin days. The space in front of the TV where we watched Nick Jr. (I still know the words to that "Red, red, red ball" song) was littered with these pieces. He liked to build his own stuff while I liked to copy the models on the box's cover. It became kind of a tradition between the two of us to play with these Legos on Christmas mornings while waiting for our parents to wake up. Over the years, though, the bricks were assimilated into the rest of my brothers' Lego collection.

Polly Pocket. I collected a lot of these, getting some of them as gifts and buying the rest with my weekly $1 allowance. My favorites were a small purple horse trailer with a saddled chocolate-colored horse that Polly could ride, the babysitting playset, the school, the mansion, and the ice cream parlor. A recurring storyline involved the floppy brown-haired one turning evil, taking over the town, stealing Polly's boyfriend--the only male figurine in my entire collection--and making everyone wear cement clothes.

Barbie. No girl's toy list is complete without this chick. I had several of the older model, before they adjusted her vital statistics to make her body more realistic. I also had the flat-chested, Skipper who didn't smile. To be honest, I didn't care how small her waistline or how big her boobs were; I just liked giving Barbie things to do in the wooden dollhouse my parents gave me. She had mostly G-rated adventures, until an older playmate took things to soap opera proportions one afternoon by introducing a teen pregnancy storyline for Babysitter Skipper. I feel somewhat traumatized on my dolls' behalf because of this.

Not really a toy: four ballerina figurines. Because they looked alike, they were sisters in my stories. The protagonist was a sitting ballerina (explained by a crippling injury), the least maarte-looking of the four. She was in love with a yellow yarn marionette I'd made. I later made a red one to play the part of lecherous antagonist.

Paradisa Lego sets (the girl-oriented Lego). I'd steal some of my brothers' bricks and male minifigs to stage pirate raids on the Paradisa resort. I had a heroine on a jetski. I was always annoyed with my youngest brother for messing up my playspace, so when I got older, I let him have the Paradisa pieces. I kind of regret this whenever I go home, go to his room, and see them gathering dust on his bookshelf.

Brown stuffed rabbit. My favorite stuffed toy to hug. Mom got him from the thrift store and was supposed to donate him along with a bunch of other toys, but I "borrowed" him from the pile and never gave him back. When I left for college, he and many other toys were hidden in the cupboard above my closet so my mom wouldn't give him away.

a Bratz Jade doll. Jade was the last doll I ever got. I was already in high school, so this cool-looking teen doll with a gang of equally cool friends appealed to me. With her sneakers and casual outfit, I made Jade out to be the athletic girl-next-door and got one of the male Bratz, Dylan, to play her fun boyfriend. But I lost all interest when the Bratz makers put out all those outrageous themed outfits and ditzy movies where Jade was a fashionista, her friends were all screeching caricatures, and Dylan was a useless goofball.