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Ed Pegg
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One item to be aware of is [Unistable Polyhedra][1]. The surface area on the projected sphere doesn't matter much if a face happens to be unstable. Also, the surface the object is tossed at matters ... pitch, felt and glass can cause a die to...
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/adf6c134-2522-4e40-9530-169a4f560c81
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/b44965b4-0486-4750-8b31-f238fc059ec4
Thanks, Thomas. I've found solutions matching everything in the paper.
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/7d6d20bd-7f17-4868-bf02-5060d954afc1
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/18003051-8b86-4622-8f54-3a2e360b8aaa
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/56a2d470-e037-4cae-b232-b4a5c2996bb5
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/64a2a7cb-6a1d-4873-a4c7-2fdc455f6350
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/d269f1e5-5dc4-48de-934d-6d4e948739cc
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/6dfe9208-ee6f-44fd-b888-62319a4f3965