Ah, I can see how to easily generate a "Thurston cut-out" of these. It is just like the icosahedral one, and like the buckyball I just posted: You just subdivide all triangles. You could then color the hexagons.
In fact, I will probably make one this evening!
Hmm, but these Goldberg polyhedra also have a slight angular deficit for each hexagon vertex, so that it becomes more spherical. It would get very messy if you also did that in the cut-out. If you leave out those angular deficits, you get large flat hexagons "painted" by sub-hexagons.
Gerard Westendorp
npub1fa…0s7kh
2024-10-28 10:01:36 UTC
in reply to nevent1q…rxn9
Author Public Key
npub1fayw49zkgcklpwmvdsplpmxgdd3xm4vdkg45vgf9ff4nzxgvr42s00s7khSeen on
wss://relay.momostr.pinkPublished at
2024-10-28 10:01:36 UTCEvent JSON
{
"id": "1545a30c8c12d869b3d5631232437a4e758448b035b428dce56a17a07bfd9c8b",
"pubkey": "4f48ea9456462df0bb6c6c03f0ecc86b626dd58db22b4621254a6b31190c1d55",
"created_at": 1730109696,
"kind": 1,
"tags": [
[
"proxy",
"https://mathstodon.xyz/@GerardWestendorp/113384469041400351",
"web"
],
[
"p",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"p",
"4f48ea9456462df0bb6c6c03f0ecc86b626dd58db22b4621254a6b31190c1d55"
],
[
"e",
"fe3d80b0ab28e25400ad6733bee6b78ab450fb75a5906c5348df8b0212b44731",
"",
"root",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"p",
"dff9dc18358b6d4fd9ef5116da29e4a6a741cc5b0929d0ae0942a6ca8d1d71dd"
],
[
"e",
"790a018fd8912bef7cded0a85070c120439dbc88fbcacf7c61a88d6d5ef74a2d",
"",
"reply",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"proxy",
"https://mathstodon.xyz/users/GerardWestendorp/statuses/113384469041400351",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/GerardWestendorp/statuses/113384469041400351",
"pink.momostr"
],
[
"-"
]
],
"content": "Ah, I can see how to easily generate a \"Thurston cut-out\" of these. It is just like the icosahedral one, and like the buckyball I just posted: You just subdivide all triangles. You could then color the hexagons.\n\nIn fact, I will probably make one this evening!\n\nHmm, but these Goldberg polyhedra also have a slight angular deficit for each hexagon vertex, so that it becomes more spherical. It would get very messy if you also did that in the cut-out. If you leave out those angular deficits, you get large flat hexagons \"painted\" by sub-hexagons.",
"sig": "2821150512ae04ece792ac02661fb1cc54a141b9181865473813fb525629b9f112a9e3adc1f8f156b99da2453f40fec2373055cfb63eafddc79d0a2ca9a62178"
}