### geometry of modular origami and extrapolating to more units

Posted:

**June 9th, 2020, 5:29 am**hey all,

this might be a dumb question but ive been making modular origami for about 9 years and I’m sort of at the point where I’m bored of making the same models over and over again. There are a bunch of 30-unit spheres that I really like and I want to extend them to 90-units or higher. I understand the geometry of the 90 unit models I have made, but I’m just wondering if most pieces can be extended to higher numbers of modules. For example, I’ve folded Tomoko Fuse’s Seastar model with 30 units, and i see how the units come together in vertices of 5, so I would assume I could create a 90 unit module by creating vertices of 6 in the buckyball configuration just like sonobe/phizz/etc. and similarly, ive loved making all sorts of phizz creations because they can combine to make toruses & spheres & almost any shape you can imagine. And I’ve always been curious why this isn’t true of lots of other modules. Because I know that the pentagon/hexagon/heptagon formations create the curvature, but that seems true of any modular piece. is there something that makes phizz units especially flexible when it comes to the variety of shapes that can be made?

and you’re probably all thinking “why don’t you just try it out?!” and my answer is that I am really limited in my supply of paper so I get really stressed out about “wasting” paper trying new modules. which I suppose is not exactly ideal for someone who wants to start experimenting. anyways, if anyone is particularly keen to explain any of these concepts that would be wonderful (and if anyone could recommend any resources— if they exist— about how units combine & the number of edges/vertices/etc.)

this might be a dumb question but ive been making modular origami for about 9 years and I’m sort of at the point where I’m bored of making the same models over and over again. There are a bunch of 30-unit spheres that I really like and I want to extend them to 90-units or higher. I understand the geometry of the 90 unit models I have made, but I’m just wondering if most pieces can be extended to higher numbers of modules. For example, I’ve folded Tomoko Fuse’s Seastar model with 30 units, and i see how the units come together in vertices of 5, so I would assume I could create a 90 unit module by creating vertices of 6 in the buckyball configuration just like sonobe/phizz/etc. and similarly, ive loved making all sorts of phizz creations because they can combine to make toruses & spheres & almost any shape you can imagine. And I’ve always been curious why this isn’t true of lots of other modules. Because I know that the pentagon/hexagon/heptagon formations create the curvature, but that seems true of any modular piece. is there something that makes phizz units especially flexible when it comes to the variety of shapes that can be made?

and you’re probably all thinking “why don’t you just try it out?!” and my answer is that I am really limited in my supply of paper so I get really stressed out about “wasting” paper trying new modules. which I suppose is not exactly ideal for someone who wants to start experimenting. anyways, if anyone is particularly keen to explain any of these concepts that would be wonderful (and if anyone could recommend any resources— if they exist— about how units combine & the number of edges/vertices/etc.)