Flexagonator and its programming language
- Generating sequence: this is where you input the flexes you want your flexagon to do. If you want a flexagon that just pinch flexes, you just write P* or P+ and that’s what you get! The difference between * and + is subtle – we’ll get to that in just a moment.
- Search flexes: a list of flexes. Whatever flexes you write here will appear as buttons on the image of the main face of the flexagon on the left, that, when pressed, perform the flex.
- Pats per side: The number of pats on the face, for example, 6 will give you a hexaflexagon, 7 a heptaflexagon, and so on.
- Center angle: the angle of one triangle at the center of the flexagon. For equilateral triangles, this is 600.
- Angle 2: the second angle if the triangle is not equilateral. The third angle is of course deduced, given that the sum of the angles must be 1800.
Let’s give it a try, shall we?Input the following generating sequence: P+. This will make a pinch flex the only flexagon. It’s always advisable to write all possible flexes in the “Search flexes” box. Even the default is not an exhausted list, so, you can copy and paste this list:
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Davidson Institute of Science Education at the Weizmann Institute of Science online course,
Flexagons Galore: Advanced Flexagon Fun
* vs +Suppose you want to create a flexagon that can perform two consecutive pinch flex around the main hinge. You want to tell flexagonator to make a structure with a pinch flex, that, when applied again, can be pinch flexed again around the same hinge. Note that with the simple tri-hexa-flexagon that you just made this cannot be done because the position of the hinge alternates after every flex. To tell the program to make a flex and apply it (theoretically), you add an asterisk after the flex, like this: P*. So, an asterisk after a flex means create the structure to support the flex and apply it (theoretically) and a plus sign means to create the flex without applying it. By “theoretically” I mean that the program doesn’t show you the flexagon after the flex is applied, it just creates the structure that can support actually doing this. For structures generated for single flexes, there is no difference between * and +, so for the tri-hexa-flexagon you just created, you could have written P*. But, for a structure that supports two consecutive pinch flexes around the same hinge you have to write: P* P*. Try it out! When you do this, you’ll get a 12-leaf flexagon. When you press the P next to the main hinge (denoted by *), you are able to pinch flex again from the same position. Also note, that this flexagon supports many other flexes as well. Contrast this flexagon with one that supports two pinch flexes without applying them by using this generating sequence: P+ P+. You’ll get the regular 9-leaf tri-hexa-flexagon again.
Flex sequence and show current scriptInstead of pressing the flex buttons on the flexagon, you can write down a sequence of flexes in the box below the flexagon. These flexes are applied one after the other in sequence, around the main hinge. With the P* P* generated flexagon, you can perform: P V St to replace the green number 2 back face, with a purple number 4 one! When you press “Show current script” you get the “hard core” programming language – that is yet another way to generate and flex flexagons. The full programming language is beyond the scope of this course, but if you’re interested you can learn it here. Instructing flexagonator to create and flex flexagons using this language, instead of the buttons in the top section, is what you can do in the second section.
Flexagons Galore: Advanced Flexagon Fun
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