ZenoRogue | Emerald Mine in {5,3,4} (version 2) @ZenoRogue | Uploaded April 2019 | Updated October 2024, 15 minutes ago.
Normally when you pick cells closer to cell A than to cell B, you get a half-space. But if you are in a highly symmetric closed hyperbolic manifold, the result looks much more interesting.
This manifold is constructed of 260 right-angled dodecahedra (using HyperRogue's "field quotient" method). Two dodecahedra A and B in distance 5 are chosen, and walls are put on the dodecahedra which are closer to B than to A. (Each dodecahedron is in distance 1 to 12 adjacent dodecahedra.)
The earlier version: youtube.com/watch?v=c5XSugCQHuo
This version improves the sight range (7 absolute units during the whole video) and stabilizes the camera (we move along a geodesic).
HyperRogue: roguetemple.com/z/hyper
Normally when you pick cells closer to cell A than to cell B, you get a half-space. But if you are in a highly symmetric closed hyperbolic manifold, the result looks much more interesting.
This manifold is constructed of 260 right-angled dodecahedra (using HyperRogue's "field quotient" method). Two dodecahedra A and B in distance 5 are chosen, and walls are put on the dodecahedra which are closer to B than to A. (Each dodecahedron is in distance 1 to 12 adjacent dodecahedra.)
The earlier version: youtube.com/watch?v=c5XSugCQHuo
This version improves the sight range (7 absolute units during the whole video) and stabilizes the camera (we move along a geodesic).
HyperRogue: roguetemple.com/z/hyper
![[360° VR] Portals to Non-Euclidean Geometries](https://i.ytimg.com/vi/bQSfzDugH7s/hqdefault.jpg "[360° VR] Portals to Non-Euclidean Geometries
This is a 360° VR version of our earlier video:https://www.youtube.com/watch?v=yqUv2JO2BCs
On this tour, portals will take us to various non-Euclidean geometries. This is not Minecraft!
A cool holonomy effect happened during this tour, but it was not explained by our guide Tehora! Have you found it? Please tell us in the comments!
Tehora Rogues channel: https://www.youtube.com/channel/UCHRkB4HgLLReBxWJwblHsjQ
Visited geometries:
* Three-dimensional Euclidean space 𝔼³ (cyan floors, music: Icy Land by Shawn Parrotee)
* Product space ℍ²×ℝ (green floors, music: Living Caves by Shawn Parrotee)
* Three-dimensional hyperbolic space ℍ³ (yellow floors, music: RLyeh by Shawn Parrotte)
* Product space 𝕊²×ℝ (blue floors, music: Ocean by Will Savino)
* Three-dimensional spherical space 𝕊³ (purple floors, music: Land of Eternal Motion by Shawn Parrotte)
* Solv (brownish floors, music: Lost Mountain by Lincoln Domina)
HyperRogue soundtrack under the Creative Commons BY-SA 3.0 license
Link to RogueViz: https://zenorogue.itch.io/rogueviz
To learn more about non-Euclidean geometry, play HyperRogue or visit our discord: https://discord.gg/8G44XkR")
