Building a 1.4m high polar zonohedron dome (&#39;zome&#39;) on Saturday. Firs...
- 2018-06-18 14:55:31+0000 - Updated: 2018-06-18 14:56:22+0000
Building a 1.4m high polar zonohedron dome ('zome') on Saturday. First strip cut out of cardboard.

Building a 1.4m high polar zonohedron dome ('zome') on Saturday. First strip cut out of cardboard.

Shared with: Public, Tim Hutton, Gerard Westendorp
- 2018-06-18 21:18:53+0000 - Updated: 2018-06-18 21:21:38+0000
This pseudosphere looks a bit like a zonohedron. I am not sure the rhombi are planar, although they have equal sides.
- 2018-06-19 09:18:51+0000
Oh, interesting, thanks. Yes, they can't be planar else the shape would be the same as a zome. After reading your link from last time I guess that means it's a Chebyshev net?
- 2018-06-19 10:27:09+0000
Yes, it is a Chebyshev net.
I think you got a discretisation of the 'Sine Gordon' equation for the top angle (alfa) of the rhombi, if you demand that the angluar deficit per area is constant, ie constant Gausian curvature.
(area is proportional to the sin(alfa)). Thats cool, because the sine gordon equaiton has solitons, which then correspond to these shapes.
- 2018-06-19 14:18:59+0000
I vaguely know of Sine Gordon as a PDE. Here's the damped version as a Ready file with a stationary soliton: https://drive.google.com/file/d/17z7190Hd-HigkwPpif6HI5KMWVD6Of5r/view?usp=sharing (I think, please check.)
But what's the connection between the solitons and the 3D shapes?

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