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Roice Nelson
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Uniform tilings of the hyperbolic plane
by Basudeb Datta and Subhojoy Gupta

Abstract. A uniform tiling of the hyperbolic plane is a tessellation by regular geodesic polygons with the property that each vertex has the same vertex-type, which is a cyclic tuple of integers that determine the number of sides of the polygons surrounding the vertex. We determine combinatorial criteria for the existence, and uniqueness, of a uniform tiling with a given vertex type, and pose some open questions.

https://arxiv.org/abs/1806.11393

h/t +Henry Segerman for sharing with me.
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Uniform tilings of the hyperbolic plane
by Basudeb Datta and Subhojoy Gupta

Abstract. A uniform tiling of the hyperbolic plane is a tessellation by regular geodesic polygons with the property that each vertex has the same vertex-type, which is a cyclic tuple of integers that determine the number of sides of the polygons surrounding the vertex. We determine combinatorial criteria for the existence, and uniqueness, of a uniform tiling with a given vertex type, and pose some open questions.

https://arxiv.org/abs/1806.11393

h/t +Henry Segerman for sharing with me.
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I found this fun blogpost a great way to become more familiar with the Johnson solids. Well worth a read!

Magforming the Johnson Solids

A blogpost about the geometrical adventures I've been having after stealing my children's toys.

https://richardelwes.co.uk/2018/05/18/magforming-the-johnson-solids/
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Mobius transformations in hyperbolic uppper space, rendered with +Roice Nelson 's shader code, I tweaked the color functions and added antialiasing and tone mapping features.

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2018/5/3
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Hyperbolic ray marching simulation, with my student Michael Woodard, and +Roice Nelson, now with Phong reflection model lighting and better UI! Try it at http://www.michaelwoodard.net/hypVR-Ray/ (wasd, arrow keys, controls tab in the top right.) Code at https://github.com/mtwoodard/hypVR-Ray
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5/1/18
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For anyone on twitter, I wrote a bot that generates 2-dimensional tilings with randomized parameters. "TilingBot" will auto-tweet once a day, though it may occasionally be more chatty when I'm having fun extending it. I hope you enjoy!

https://twitter.com/tilingbot
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A wonderful, interactive writeup about visualizing Coxeter groups, polytopes in particular.
I have written a blog post on 'Building 4D Polytopes'. This actually goes back to a Fractal Forums discussion back in 2012, where Knighty came up with a clever scheme for ray marching polytopes. It also discusses the mathematics behind Jenn 3D (a tool for creating explicit geometry).

It is probably my most ambitious post yet - lots of interactive WebGL components - which also means it not very mobile friendly, I'm afraid.

The post can be found here:
https://syntopia.github.io/Polytopia/polytopes.html

Please let me know if you have ideas for improvements or corrections!
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Finally took some time to get MagicTile building for Macs.
http://roice3.org/magictile/downloads/mac.htm
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