Just as you wanted, here we try to explain the mysterious Nil geometry! Nil is one of the eight Thurston geometries. Thurston geometries are used to classify three-dimensional manifolds. Nil is anisotropic, which means that the directions are not equivalent: the "up/down" direction acts differently than north/east/south/west directions. Presented by Tehora Rogue. Links: Hyperbolic geometry: * Temple of Cthulhu in "rectangles on horospheres" (run HyperRogue with arguments "-geo rect -W Temple -rch -noplayer -sight3 3 -smartlimit 100000 -genlimit 100000") * Right-angled pentagon:    • Right-angled pentagon   * Portals to hyperbolic and other geometries: https://www.youtube.com/watch?v=yqUv2JO2BCs * Play HyperRogue for more hyperbolic geometry! Impossible structures in Nil: * Ascending and Descending in Nil: https://www.youtube.com/watch?v=DurXAhFrmkE * Impossible ring: https://www.youtube.com/watch?v=ztodGQDK810 / https://www.youtube.com/watch?v=3WejR74o6II * Impossible triangle in Nil geometry: https://www.youtube.com/watch?v=YmFDd49WsrY / https://www.youtube.com/watch?v=RPL4-Ydviug / https://www.youtube.com/watch?v=lWbrHAYsQk4 * See also the RogueViz demo "Playing with Impossibility" https://zenorogue.itch.io/rogueviz (or the recording https://www.youtube.com/watch?v=PD_ubxntGeU ) The Nil Rider game shown is a work in progress. Should be available soon! EDIT: https://zenorogue.itch.io/nil-rider More related stuff: * Perpetuum Mobile in Nil: https://www.youtube.com/watch?v=mxvUAcgN3go We use: * the RogueViz engine: roguetemple.com/z/hyper/rogueviz.php * 3D model of Ascending and Descending by Lucian B.: https://3dwarehouse.sketchup.com/model/3e6df6c24a95f583cefabc2ae69d584c/MC-Escher-Ascending-and-Descending * HyperRogue soundtrack under the Creative Commons BY-SA 3.0 license (R'Lyeh by Shawn Parrotte and Lost Mountain by Lincoln Domina)