Talk:7-limit symmetrical lattices - Revision history

FloraC: FloraC moved page Talk:The Seven Limit Symmetrical Lattices to Talk:7-limit symmetrical lattices: For obvious reasons

2025-09-03T13:31:54Z

FloraC moved page Talk:The Seven Limit Symmetrical Lattices to Talk:7-limit symmetrical lattices: For obvious reasons

← Older revision	Revision as of 13:31, 3 September 2025
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Sintel at 22:00, 26 April 2025

2025-04-26T22:00:58Z

← Older revision		Revision as of 22:00, 26 April 2025
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			== Some notes ==

			Interesting page, actually. I'm trying to work through it bit by bit to make sure I understand it.
			The page doesn't really explain what is "symmetric" about these lattices. The original lattice is of course already full of symmetries since it's just the usual cubical lattice.

			For the first part, there is some bit about coming up with various norms and then comes to the conclusion that you can make a cuboctahedron out of the 7-odd limit.
			I feel like you can explain this quite simply by considering the transformation:

			:<math>
			A = \begin{bmatrix}
			0 & -1 & -1 \\
			-1 & 0 & -1 \\
			-1 & -1 & 0 \\
			\end{bmatrix}
			</math>

			Computing explicitly:

			:<math>
			\begin{aligned}
			A[1,0,0]^\mathsf{T} &= [0, -1, -1]^\mathsf{T} \\
			A[0,1,0]^\mathsf{T} &= [-1, 0, -1]^\mathsf{T} \\
			A[0,0,1]^\mathsf{T} &= [-1, -1, 0]^\mathsf{T} \\
			A[1,-1,0]^\mathsf{T} &= [1,-1,0]^\mathsf{T} \\
			A[1,0,-1]^\mathsf{T} &= [1,0,-1]^\mathsf{T} \\
			A[0,1,-1]^\mathsf{T} &= [0,1,-1]^\mathsf{T} \\
			\end{aligned}
			</math>

			Which are the vertices of a cuboctahedron, as we wanted.

			– [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 22:00, 26 April 2025 (UTC)

Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:44Z

1 revision imported: Moving archived Wikispaces discussion to subpage

← Older revision	Revision as of 18:02, 1 October 2018
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Wikispaces>FREEZE at 18:01, 1 October 2018

2018-10-01T18:01:16Z

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	~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~		{{WSArchiveLink}}
	~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~
	~~----~~

	~~== Question about [a b c] notation ==~~
	~~I'm confused by this sentence:~~

	"The 4:5:6:7 major tetrad consists of the notes \|* 0 0 0>, \|* 1 0 0>, \|* 0 1 0>, and \|* 0 0 1>; the centroid of this is \|* 1/2 1/2 1/2>; similarly the centroid of 1/4:1/5:1/6:1/7 is \|* -1/2 -1/2 -1/2>. If we shift the origin to \|* 1/2 1/2 1/2>, major tetrads correspond to [a b c], a+b+c even, and minor tetrads to [a-1 b-1 c-1], a+b+c even, which is the same as saying [a b c], a+b+c odd"

	~~This [a b c] notation wasn't defined anywhere on the page. What does it mean, and how does it define a tetrad, rather than an interval?~~

	~~- '''mbattaglia1''' September 15, 2011, 12:29:35 AM UTC-0700~~
	~~----~~
	~~I'm going to rewrite this old posting.~~

	~~- '''genewardsmith''' September 15, 2011, 09:16:55 AM UTC-0700~~
	~~----~~

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

New page

= ARCHIVED WIKISPACES DISCUSSION BELOW =
'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
----

== Question about [a b c] notation ==
I'm confused by this sentence:

"The 4:5:6:7 major tetrad consists of the notes |* 0 0 0>, |* 1 0 0>, |* 0 1 0>, and |* 0 0 1>; the centroid of this is |* 1/2 1/2 1/2>; similarly the centroid of 1/4:1/5:1/6:1/7 is |* -1/2 -1/2 -1/2>. If we shift the origin to |* 1/2 1/2 1/2>, major tetrads correspond to [a b c], a+b+c even, and minor tetrads to [a-1 b-1 c-1], a+b+c even, which is the same as saying [a b c], a+b+c odd"

This [a b c] notation wasn't defined anywhere on the page. What does it mean, and how does it define a tetrad, rather than an interval?

- '''mbattaglia1''' September 15, 2011, 12:29:35 AM UTC-0700
----
I'm going to rewrite this old posting.

- '''genewardsmith''' September 15, 2011, 09:16:55 AM UTC-0700
----