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Things You've Been Doing Other Than CGoL

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Re: Things You've Been Doing Other Than CGoL

Postby gameoflifeboy » July 29th, 2017, 5:36 pm

muzik wrote:I can't be the only one who finds it weird and confusing that there exists no star polyhedron {5/2,5/2}?

Wikipedia says it counts as a failed star polyhedron, since it doesn't eventually close.


I think I can explain this. It looks like I'm turning into "that one guy who always answers when people have questions about geometry" :lol: .

I used to find the nonexistence of {5/2, 5/2} weird and confusing too, but it's really no stranger than the fact that {5/2, 4} doesn't exist. It just appears that it might because all of the subsymmetries implied by the Schlafli symbol (pentagonal and digonal/rectangular) exist as subsymmetries of dodecahedral symmetry.

Any nonconvex uniform polytope that has a kaleidoscopic (Wythoffian) construction--and therefore a Coxeter diagram--and does not overlap itself infinitely, must have a symmetry describable by a convex kaleidoscopic consruction (proof?). This means that nonconvex regular polytopes never "make" their own symmetry, they always follow the symmetries of convex polytopes. In this case, {5/2, 3} and {5/2, 5} both happen to close under the symmetry of {5, 3}, icosahedral symmetry. {5/2, 5/2}, however, does not, and there is no other symmetry that it can close under, as it would need to have a pentagonal subsymmetry. This is also why the only regular hyperbolic star tessellations are {n/2, n} and {n, n/2} for odd n greater than 6, as these are the only kaleidoscopic constructions that lend themselves to regular polytopes and a regular symmetry, namely {n, 3}.

Another way to think of it is that it doesn't exist because its conjugate* would be {5, 5}, which is hyperbolic and obviously doesn't close either.

Finding all the possible Coxeter diagrams that close under a certain symmetry is difficult (for me), but it can be done by realizing that their omnitruncates** are all facetings*** of each other if given the right edge lengths; each ring in the Coxeter diagram represents a different type of edge, and the edges of each type can have their length changed independently of those of any other type.

Dr. Richard Klitzing has a better way to find these, by "adding" the Coxeter diagrams (called Dynkin diagrams on the website), but I can't really understand it. It is described here: https://bendwavy.org/klitzing/explain/schwarz.htm

*A conjugate of a uniform polytope is one that, roughly, can be constructed by taking regular polygonal subsymmetries (usually on the faces or face figures, which are vertices in 3D) and "wrapping" the symmetry a different number of times. For example, the great dodecahedron {5, 5/2} can have its pentagonal faces doubly wrapped into pentagrammic faces and its pentagrammic vertex figures doubly wrapped into pentagonal ones. This produces the small stellated dodecahedron {5/2, 5}, thus the great dodecahedron and small stellated dodecahedron are conjugates. Taking a polytope's conjugate changes the circumradius and coordinates into their algebraic conjugates; numbers that are roots of the same polynomial.

It is also worth noting that the pentagonal faces and the pentagrammic vertices of the great dodecahedron must change together, as they can be "paired up"; each face lies directly under a vertex. On the other hand, in the square tiling {4, 4} (for example), squares and square-symmetry vertices cannot be paired up, meaning that they can be re-wound independently of each other. If the squares and/or vertices get re-wound thrice, it could lead to {4/3, 4}, {4, 4/3}, or {4/3, 4/3}--but these are all also the square tiling, so this creates no new tessellations.

**The omnitruncate of a Coxeter diagram is the shape made when every node in the diagram is ringed.

***Faceting: a polytope which shares the same vertices as another polytope.
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » July 30th, 2017, 10:03 pm

How would {1,2} and {2,1} look as tesselations of a sphere?
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Re: Things You've Been Doing Other Than CGoL

Postby lifeisawesome » December 7th, 2017, 10:11 am

Black MIDIs. The largest one I have made has 5 million notes.

Too bad it's just spam...
--Szymon Bartosiewicz
favorite pattern:
x = 2, y = 2, rule = B25/S3a
2o$2o!
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Re: Things You've Been Doing Other Than CGoL

Postby blah » December 9th, 2017, 12:54 pm

Making a new version of Reasoning Realm.
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » December 24th, 2017, 6:30 pm

trying to finish off that pokemon diamond i got four years ago.
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » March 12th, 2018, 1:36 pm

Currently on the hunt for numerous old Minecraft versions that got gradually lost over the years.
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Re: Things You've Been Doing Other Than CGoL

Postby jimmyChen2013 » March 12th, 2018, 10:43 pm

muzik wrote:Currently on the hunt for numerous old Minecraft versions that got gradually lost over the years.

How old?
i got a luncher that got all the older versions
Failed Replicator!
x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo$obo$bobo$2bo!

(That I wish was not failed D:)
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » March 13th, 2018, 7:27 am

jimmyChen2013 wrote:
muzik wrote:Currently on the hunt for numerous old Minecraft versions that got gradually lost over the years.

How old?
i got a luncher that got all the older versions

What ones exactly?
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Re: Things You've Been Doing Other Than CGoL

Postby Saka » March 13th, 2018, 8:29 am

I've been growing plants, especially orchids.
Proud owner and founder of Sakagolue
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)
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Re: Things You've Been Doing Other Than CGoL

Postby Cclee » March 13th, 2018, 8:47 am

muzik wrote:
jimmyChen2013 wrote:
muzik wrote:Currently on the hunt for numerous old Minecraft versions that got gradually lost over the years.

How old?
i got a luncher that got all the older versions

What ones exactly?

All of them. From the launcher you have to go into launch settings and then select the version from there so you cam create a file for Minecraft from that version then back at the news bar you have to click the arrow select next to launch and click your version file then launch it
^
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Re: Things You've Been Doing Other Than CGoL

Postby Majestas32 » March 13th, 2018, 9:41 am

Those aren't all the versions tho.

About half the alpha 1.0 versions are still missing
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » March 13th, 2018, 12:17 pm

Cclee wrote:
muzik wrote:
jimmyChen2013 wrote:How old?
i got a luncher that got all the older versions

What ones exactly?

All of them.

So where are Alpha 1.0.0, 1.0.1, 1.0.2, 1.0.3, 1.0.5, 1.0.6, 1.0.7, 1.0.8, 1.0.9, 1.0.10, 1.0.12, 1.0.13, 1.0.17, 1.1.1, 1.2.1, 1.2.4 and various other versions then?
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Re: Things You've Been Doing Other Than CGoL

Postby Cclee » March 14th, 2018, 9:48 am

muzik wrote:
Cclee wrote:
muzik wrote:What ones exactly?

All of them.

So where are Alpha 1.0.0, 1.0.1, 1.0.2, 1.0.3, 1.0.5, 1.0.6, 1.0.7, 1.0.8, 1.0.9, 1.0.10, 1.0.12, 1.0.13, 1.0.17, 1.1.1, 1.2.1, 1.2.4 and various other versions then?

There used to be a setting for turning on alpha and even beta versions is that still there?
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Re: Things You've Been Doing Other Than CGoL

Postby Majestas32 » March 14th, 2018, 10:06 am

Yes. But not all the alpha versions are available. Only about half.

And pre-alpha is even worse. There are 0 indev and only 1 infdev version in the launcher.

I think even release 1.5.0 is not in the launcher
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Re: Things You've Been Doing Other Than CGoL

Postby fluffykitty » March 14th, 2018, 3:00 pm

Also almost no snapshots
I like making rules
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Re: Things You've Been Doing Other Than CGoL

Postby Majestas32 » March 14th, 2018, 7:07 pm

Well that's a given. Thou ial am preserving as many as possible 1.13 snaps
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » March 15th, 2018, 7:31 am

Majestas32 wrote:Well that's a given. Thou ial am preserving as many as possible 1.13 snaps

Can't you still download the jars from the website though?
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Re: Things You've Been Doing Other Than CGoL

Postby Majestas32 » March 15th, 2018, 9:53 am

For snapshots? Not for past versions like 1.12
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » March 15th, 2018, 10:07 pm

Majestas32 wrote:For snapshots? Not for past versions like 1.12

...just go to the wiki pages for said snapshots and download the jars?
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » March 18th, 2018, 7:36 pm

Well here's a complete list of the alpha versions that aren't available:

1.0.0
1.0.1
1.0.2
1.0.2_01
1.0.2_02
1.0.3
1.0.5
1.0.6
1.0.6_01
1.0.6_02*
1.0.6_03
1.0.8
1.0.9
1.0.10
1.0.12
1.0.13
1.0.13_01
1.0.13_02*
1.0.14_01
1.0.16_02
1.0.17
1.0.17_01*
1.0.17_03
1.1.1
1.2.1*
1.2.3_03*
1.2.4*

* No solid proof of existence
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Re: Things You've Been Doing Other Than CGoL

Postby BlinkerSpawn » March 20th, 2018, 9:08 am

Submitting incorrect answers to Project Euler
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Things You've Been Doing Other Than CGoL

Postby Rhombic » March 20th, 2018, 7:47 pm

Planning my trip to Prague... :)
SoL : FreeElectronics : DeadlyEnemies : 6a-ite
what is “sesame oil”?
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Re: Things You've Been Doing Other Than CGoL

Postby wwei23 » April 21st, 2018, 11:22 pm

lifeisawesome wrote:Black MIDIs. The largest one I have made has 5 million notes.

Too bad it's just spam...

Video?
I took Yamboo Kalinka and unsilenced the MIDI art:
https://www.youtube.com/watch?v=9oeDxeWI8XQ
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Re: Things You've Been Doing Other Than CGoL

Postby muzik » May 1st, 2018, 8:27 am

What is the equation of the curve present in x^y=y^x?
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