Mathematics, game development, art, roguelikes, hyperbolic geometry. Sometimes all at once.
Mar 25, 2023 • 13 tweets • 6 min read
The dual of the famous new hat tiling. Twenty-Seven on the HyperRogue discord used dual to make it easier to tell which tiles are adjacent, but in HR 12.1k it looked "cursed" because the hats were not centered well. Dui Mauris Football had an idea to animate the center changes...
Here the center movement is simpler, but we change the hats (like in
I see no images of regular star pseudohedra in the Internet, so let's change this. This is {7,7/2} in the Poincare ball model. Its faces are heptagons and they intersect each other (a similar structure to a great dodecahedron). It looks some some kind of a fantasy shield. (1/6)
And here is its dual, {7/2,7}. The faces of this are star heptagons. (2/6)
May 6, 2020 • 6 tweets • 3 min read
We have already see this: the space of rotations of the sphere. As well known in 3D graphics, this space is the same as unit quaternions, i.e., a 3-sphere (with opposite points identified). Today, we will modify this to get a new geometry! (1/6+)
The straight lines you see are called fibers. We change the geometry by stretching the metric along the fibers. As if the speed of light was slower/faster along the fiber, and light still took the fastest route, as usual.
