# Check out this new web toy I made. Expl

Check out this new web toy I made. Explore the tilings of the hyperbolic plane by moving your mouse around to smoothly change the curvature of space. Take the curvature positive to discover the polyhedra.

### timhutton/hyperplay

Shared with: Public, Tim Hutton, Christopher Hanusa, Owen Maresh, Shamanic Harmonics, Refurio Anachro, John Baez

+1'd by: Andrew King, Mikael Hvidtfeldt Christensen, Eran Agmon, Roberto Santander, scott stensland, Luis Guzman, Mosh Jahán, Timothy Gowers, Nancho Alvarez, Refurio Anachro, Richard Green, Christopher Hanusa, David Moore, Owen Maresh, Hunter Yavitz, Doug Hackworth, Roice Nelson, Dmitry Shintyakov, Henry Segerman, Whitt Whitton, Dr Nick Hammond, Carlos Portela, Jonathan Stanley, Torolf Sauermann, Scott Vorthmann, Aistis Raulinaitis, Michael Velik

*This post was originally on Google+*

https://github.com/dmishin/Pentagrid/releases

And I have even found some spaceships: http://dmishin.blogspot.ru/2011/10/hyperbolic-cellular-automation.html

Unfortunately, {5;4} tiling appeared boring: rules with spaceships are instable. I tried to write a simulator for the {4;5} tilings, but failed to develop a method of cell addressing.

> I think the great icosahedron is there too, at 0.98 in the {3,q} family.

Of course it is! I would have missed that one, thanks!

http://en.wikipedia.org/wiki/Schlegel_diagram

-1.115 Schlegel diagram of tetrahedron;

-1.054 Schlegel diagram of icosahedron

0.61 icosahedron,

0.815 octahedron

0.944 tetrahedron

0.983 first stellation of the dodecahedron

It allows you to share the link directly to shapes you find. e.g. {5,3,4} is here: http://timhutton.github.io/hyperplay/index_sliders.html?f0=1.176&f1=0.714&f2=-0.347 Here's {4,3,4}: http://timhutton.github.io/hyperplay/index_sliders.html?f0=1.4142&f1=1.1547&f2=0

The curvatures are now based off the edge length of 1. Previously it was based on the polygon circumcircle radius of 1, which wasn't really sensible in this new multi-dimensional setting.

Share the shapes you find!

(dodecahedral type tiling)

and http://timhutton.github.io/hyperplay/index_sliders.html?f0=0.398&f1=0.633&f2=-0.163

(hair!)

~~Oh heck, I've got a bug in the curvatures. No more sharing links until it's fixed please! Sorry! Hold the line.~~+Christopher Hanusa your amusing hair one was something like this I think: http://timhutton.github.io/hyperplay/index_sliders.html?f0=0.413&f1=0.403&f2=-0.066

which you can then bend into the first stellation of the dodecahedron here: http://timhutton.github.io/hyperplay/index_sliders.html?f0=1.903&f1=1.699

http://timhutton.github.io/hyperplay/index_sliders.html?f0=1.414&f1=1.155&f2=-1.414

https://github.com/timhutton/hyperplay/wiki

Anyone is welcome to add more. Just make a github account and edit directly or send them to me.

It has positive curvature, so it closes back on itself and actually makes a polyhedron in 4D made of 600 tetrahedra joined face-to-face: http://en.wikipedia.org/wiki/600-cell

It would be great to be able to freeze the geometry and export -

If a all possible, Encapsulated Post Script so it can be vector and used in Illustrator.

Since it is also wrapping 3D maybe an export to .stl or .obj also?

THANKS again for this!