Post #3078236
2025-05-22 05:28 UTC
@rasjor@mathstodon.xyz thanks again. The rendering part is relatively straightforward. If you want to hear about the extra algorithm, I enumerated all the nets of the dodecahedron, and programmatically checked which nets will cover all the faces of the great dodecahedron by “overfolding”. Only about 0.1% of the dodecahedron nets cover all faces of the great dodecahedron. Those are rare cases, and the common nets won’t work. Interestingly, 100% of the icosahedral nets can overfold into the great icosahedron covering all the faces.
Replies (1)
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@rasjor@mathstodon.xyz 2025-05-23 05:38
@nanma80@mathstodon.xyz That is interesting, even the thought that there are this many dodecahedral nets is totally counterintuitive to me. In regards to the difference between great dodecahedron and great icosahedron, I would imagine, that it has something to do with the prior being of genus 4 and the latter of genus 0. Thus, I assume, the great dodecahedron having to be "cut" open, when transforming from the dodecahedron and the great icosahedron is merely "twisted" into place.