User talk:Sycamore916/Sandbox/Tunnellings of Johnson solids

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Second tunnelling of the bilunabirotunda[edit source]

H A M 1, thanks for the contributions. What is the second tunnelling of the bilunabirotunda? 01:53, 5 February 2023 (UTC)

excavated with a z4 in a different orientation H A M 1 (talk) 02:08, 5 February 2023 (UTC)
I think only one of those actually works. Z4 is built from excavating a bilunabirotunda so one of the orientations ends up sharing 4 triangular faces with the bilunabirotunda, and the result is disconnected. Sycamore916 (talk) 02:17, 5 February 2023 (UTC)

I'm going to stop counting[edit source]

When I started this I figured there would be a couple of cases with extremely large numbers due to combinatorics and mostly we'd have a handful. However It is clear to me that almost everything that can be tunnelled has a lot of tunnels. The truncated cube likely has over 100, and its augmented forms have way more. And that is one of the cases I didn't think would have many. There are probably only a few with counts between 1 and 99. Most of these solids are extremely boring excavations and augmentations of existing toroids. So instead of spending time counting the grains of sands in the ocean (this a bit hyperbolic, there's only a couple sextillion Q-convex Stewart toroids) I am going to just include a couple of minimal cases. I'm going to include 1. the tunnelling with the largest volume 2. the tunnelling with the smallest volume 3. the tunnelling with the fewest faces and all of those again for the maximum genus. This will mean up to around 6 (more if I feel like pointing out ties) polyhedra for each hull. Which should make things much more manageable while still making this a useful reference. 66.65.51.145 22:31, 6 February 2023 (UTC)