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14:46:26 <esolangs> [[APOL]] https://esolangs.org/w/index.php?diff=93140&oldid=92516 * Ginger Industries * (+148)
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15:35:31 <esolangs> [[APOL]] https://esolangs.org/w/index.php?diff=93141&oldid=93140 * Ginger Industries * (+234)
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18:42:40 <sgji> riv, yes they would be rolled onto a 3d plane, which would appear "flat" to a 4d creature in a sense (a 4d creature could see all of a 3d shape at once like how we can see all of a 2d shape at once)
18:43:51 <sgji> it would look very weird to a 3d observer lol, the shape would seemingly come in and out of existance rapidly as it passes through a 3d slice
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18:45:49 <Corbin> https://en.wikipedia.org/wiki/Tesseract#Net has some nice animations for the 4D hypercube.
18:48:41 <riv> so we are looking for isotopic polytopes
18:49:09 <riv> these correspond to fair dice
18:50:58 <sgji> i think its just shapes made of the same facets connected the same way to eachother?
18:51:44 <sgji> 4d probably has a lot more than 3d
18:52:47 <riv> yeah the facets are in a transitive symmetry group
18:53:01 <riv> so you can rotate any one to any other and the shape is the same
18:53:30 <sgji> https://cormullion.github.io/assets/images/pentachoron/showall-pentachoronmovie.gif here is a good gif showing rotating 3d projection of the pentachoron (pentachoron (4-simplex) is 5 tetrahedrons)
18:53:42 <sgji> multiple rotations
18:54:31 <riv> so this can roll a 5
18:55:32 <sgji> n-simplexes can roll up to an n+1
18:55:39 <sgji> i think they are fair in every dimension
18:55:47 <sgji> that is every n-simplex is fair
18:58:36 <riv> we need it to be convex too
18:59:00 <riv> i always though the self intersecting shapes should be reject outright.. dunno why people include them
18:59:16 <sgji> http://www.polytope.net/hedrondude/dice.htm here is a page with some good info on dice in different dimensions
19:00:06 <sgji> the 4-simplex is convex, the net may look concave but i assure you when you fold it up into the 4th dimension it becomes convex
19:01:40 <sgji> just like how a cube's 2d net doesnt look convex but is when you fold it into a cube
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19:44:32 <b_jonas> sgji: I don't think that's a good description. the planar net of a cube fods onto the *surface* of a cube, not the whole cube, and that surface is very much not convex. indeed, the net of a regular tetrahedron is convex, but when you fold it up, the surface is no longer convex, there's a big hole in the middle.
19:48:54 <b_jonas> that said, yes, if you fold out the surface of a regular 5-cell to flat space, it won't be convex
19:49:49 <sgji> i was referring to the shape that is filled in
19:50:59 <sgji> i know folding a net will make it hollow, but that is kinda irrelevant imo
19:54:03 <sgji> because we were talking about fair dice
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