Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: first shape discovered by a computer
Date: Wed, 21 Aug 2024 12:31:18 -0700
Organization: A noiseless patient Spider
Lines: 45
Message-ID: <va5fa7$3vq0v$2@dont-email.me>
References: <va3vfs$3onti$1@dont-email.me> <va41nq$3ov1e$2@dont-email.me>
 <va41to$3ov1e$3@dont-email.me> <va4m2v$3rq6i$1@dont-email.me>
 <va4q3m$3scne$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Wed, 21 Aug 2024 21:31:20 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="a81bdbcc5663df071c60bf99d403b45a";
	logging-data="4188191"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18XMuNN8gHf9TVkRaRMRn7zZpxzc1zVtuI="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:ENyxFazRBpErbShqGIY4rtmZRhg=
In-Reply-To: <va4q3m$3scne$1@dont-email.me>
Content-Language: en-US
Bytes: 2825

On 8/21/2024 6:29 AM, sobriquet wrote:
> Op 21/08/2024 om 14:20 schreef sobriquet:
>> Op 21/08/2024 om 08:36 schreef Chris M. Thomasson:
>>> On 8/20/2024 11:33 PM, Chris M. Thomasson wrote:
>>>> On 8/20/2024 10:55 PM, sobriquet wrote:
>>>>>
>>>>> Hi!
>>>>>
>>>>> https://www.desmos.com/3d/t5fsaljsmh
>>>>>
>>>>> The shape is comprised of 12 pyramids that come in two varieties, 
>>>>> but they all appear to have the same volume.
>>>>
>>>> It looks like a unit 5-gon in the xy plane at (x, y, 0) with each 
>>>> vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
>>>
>>> Not quite... Like two 5 gons one on the xy plane and one on the xz 
>>> plane rotated by pi / 2. I need to take a closer look and try to 
>>> recreate it on my end. Fun. Thanks for the post. Might have some more 
>>> time tonight.
>>
>> It's the shape with the biggest volume one can obtain with 8 vertices 
>> on the unit sphere.
>>
>> I got the coordinates for the vertices from the paper referenced in 
>> the recent Matt Parker video about the shape.
>>
>> https://www.youtube.com/watch?v=XZy3rXr2yeM
>>
>> https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf
>>
>>
>> When I computed the volume of the shape that has an isosceles
>> triangle as the base for the pyramid, it seemed to give the
>> impression that it's a twelfth of the total volume, implying
>> that the other pyramid shape with a scalene triangle base has
>> the same volume.
>>
>> https://www.desmos.com/calculator/stjrx6qsxt
> 
> I think I got the exact coordinates for the vertices now.
> 
> https://www.desmos.com/3d/xaxwkqwgw3

Cool! Thanks Man. :^)