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 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 for sharing with me.
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The Illustrating Mathematics programme, to run at ICERM in Fall 2019, has five postdoctoral positions now posted on MathJobs. Please consider applying yourself, or telling your colleagues about these positions.

https://icerm.brown.edu/programs/sp-f19/
https://www.mathjobs.org/jobs/jobs/11969
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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.

2018/5/3
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Hyperbolic ray marching simulation, with my student Michael Woodard, and , 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
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!

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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!