Uploaded May 2020 | Updated September 2026, 2 weeks ago
Let's return to the stretched spherical geometry, but with another scene!
Stretched spherical geometry explained in youtu.be/zwRKzaE_7Mo ; this is the same scene as in youtu.be/XUIYga-AfLI . It is possible to arrange the 120-cell in such a way that every dodecahedron has a pair of faces which is orthogonal to the fiber. In this video, we fill four of them.
In the first scene we have k²=0.5 and go along the fiber.
In the second scene we change the metric only slightly (k²=0.975). To all the "usual" effects of spherical geometry, we add the effect of hitting different places after going around the sphere, caused by stretching the metric.
In the third scene, the fibers are very stretched (k=0.1).
In the fourth scene, k²=0.5 again, but not going along the fiber.
In the fifth scene, we change k² from 2 to .004.
In the sixth scene, k²=0.975 (not going along the fiber) and in the seventh scene, k²=2.
Let's return to the stretched spherical geometry, but with another scene!
Stretched spherical geometry explained in youtu.be/zwRKzaE_7Mo ; this is the same scene as in youtu.be/XUIYga-AfLI . It is possible to arrange the 120-cell in such a way that every dodecahedron has a pair of faces which is orthogonal to the fiber. In this video, we fill four of them.
In the first scene we have k²=0.5 and go along the fiber.
In the second scene we change the metric only slightly (k²=0.975). To all the "usual" effects of spherical geometry, we add the effect of hitting different places after going around the sphere, caused by stretching the metric.
In the third scene, the fibers are very stretched (k=0.1).
In the fourth scene, k²=0.5 again, but not going along the fiber.
In the fifth scene, we change k² from 2 to .004.
In the sixth scene, k²=0.975 (not going along the fiber) and in the seventh scene, k²=2.
