Uploaded February 2020 | Updated September 2026, 3 weeks ago
Suggested by Owen Maresh: twitter.com/graveolens/status/1227733337025974273
See youtube.com/watch?v=YmFDd49WsrY for more information
Quotient space used: 0.9 x 9.0 x 0.81
Suggested by Owen Maresh: twitter.com/graveolens/status/1227733337025974273
See youtube.com/watch?v=YmFDd49WsrY for more information
Quotient space used: 0.9 x 9.0 x 0.81








![Can we simulate spherical geometry in Euclidean space?
Three-dimensional spherical space can be created from 120 spherical dodecahedra. Four of these are filled. In the first part of the video, we see the effects mentioned in https://youtu.be/leuleS9SpiA
Can we simulate these effects using an Euclidean game engine and portals? The remaining two parts of the video show that this does not work, but they should still be fun!
In the second part, we construct the same scene from 120 Euclidean dodecahedra. Some of the spherical effects can be seen if you look close enough. This looks like some cool abstract art, but it does not work very well as a simulation of 𝕊³.
The edges look strange because we have only 349.695° of space around them.
In the third part, we follow the suggestion of Jos Leys [ http://www.josleys.com/article_show.php?id=83 ] we attempt to construct the scene from the stereographic images of spherical dodecahedra.
This concentrates the curvature on faces instead of edges [ http://geometrygames.org/HyperbolicBlanket/ ].
Again, this looks more like abstract art than 𝕊³. Can we simulate spherical geometry in Euclidean space?](https://i.ytimg.com/vi/XUIYga-AfLI/mqdefault.jpg)

