Sunday, February 15, 2026
Accuracy
"Pray for the grace of accuracy." — Robert Lowell
From Snaith's pages 76 and 77 —
Compare and contrast . . .
Wikipedia on the numbers of cubies and facelets —
"The puzzle consists of 26 unique miniature cubes,
also known as 'cubies' or 'cubelets'."
"A 3 × 3 × 3 Rubik's Cube consists of 6 faces, each with
9 colored squares called facelets, for a total of 54 facelets."
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Saturday, February 14, 2026
Friday, February 13, 2026
Geometry for Friday the 13th
The previous post — "Cube Space" — and today's date
suggest a review of the 13 symmetry axes of the cube.
Related geometry —
|
By NotebookLM today — Symmetry in Finite Geometry and Combinatorial Design The provided sources explore the mathematical and artistic intersections of finite geometry, specifically focusing on the Cullinane diamond theorem and its square-based representations of PG(3,2). By utilizing 4×4 and 4×6 arrays, these works illustrate how combinatorial designs, such as Latin squares and Miracle Octad Generators, relate to highly symmetric structures like the Mathieu group M24 and the binary Golay code. The texts demonstrate that properties of symmetry, such as the affine group AGL(4,2), govern both abstract group theory and visual patterns found in puzzles, quilt designs, and sphere packings. This framework extends into coding theory and quantum mechanics, where geometric "bricks" and "lines" help simplify the analysis of complex lattices and error-correcting systems. Ultimately, the collection bridges rigorous algebraic abstraction with interactive visualization, showing that the logic of finite space underpins both mathematical truth and aesthetic form. |
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Cube Space
Theorem:
Some large natural symmetry groups of the sets of 8, 16, 32, or 64 points
in Euclidean space that are located at the vertices of a cube in 3, 4, 5. or 6
dimensions are generated by, respectively, arbitrary permutations of
parallel edges or parallel faces or parallel cubes or parallel hypercubes .
(For an example, see Diamond Theory in 1937.)
Illustration of related group actions:
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Monday, February 9, 2026
The Tesseract Theorem
The natural symmetry group of the 16 vertices of a tesseract
is generated by arbitrary permutations of parallel faces and
is of order 322,560.
(This is an abstract version of the Cullinane diamond theorem.)
For the corresponding cube theorem, see Cube Space.
Some backstory . . .
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Monday, September 15, 2025
Tuesday, September 2, 2025
Back-to-School Supplies for Nevermore Academy
"The Accountant 3" —
Bonnie and Clyde with the Purloined Letter
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Thursday, July 31, 2025
Obit headline: “Provocative!”*
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Sunday, September 1, 2024
Sunday Best Meets Sunday Bester
Sunday Best: The link Sunday Art from the previous post.
Sunday Bester: The author Alfred Bester in this journal.
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Saturday, August 31, 2024
Annals of British Humor
The date of the the above photo, November 8, 2015, suggests a look
at this journal on that date. See Sunday Art.
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Script Idea for Harlan Kane:
The Timeless Meets Time
"kalosmi lokaksaya krt pravrddho"
Also on July 13, 2023 . . .
From the Publications webpage of Dan Gordon —
Math Databases on the Cheap,
lightning talk at LuCaNT, July 2023.
Background from 2022 —
Gordon's informative webpage on mathematical repositories:
https://ljcr.dmgordon.org/cwm/jupyter_book/math_repos.html.
See also ICERM in this journal on November 14, 2012.
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The Timeless Meets Time
The Timeless Meets Time
Wednesday, July 10, 2024
Hexagram 52: Ken
Today's description of Dartmouth College as a "gin-soaked gutter"
by Margaret Soltan (i.e., University Diaries) suggests a review:
Monday, November 14, 2022
|
See also "KenKen" and today's previous post.
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Wednesday, July 3, 2024
Mathematics for Tricksters:
“Nothing Ventured, Nothing Gained!”
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“Nothing Ventured, Nothing Gained!”
“Nothing Ventured, Nothing Gained!”
Vedic Carnival: “Hey Rubik!” *
The Moolakaprithi Cube (as opposed to Rubik's Moola Cube ) —
"The key to these connections lies in a 3 x 3 x 3 cube, which
in Vedic Physics, forms the Moolaprakriti, a key component of
the Substratum, the invisible black hole form of matter."
— viXra.org, "Clifford Clock and the Moolakaprithi Cube"
* See Wikipedia.
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Tuesday, July 2, 2024
Chinatown
|
Updated 8:18 PM EDT, Tue July 2, 2024 "Robert Towne, the Oscar-winning screenwriter of a number of acclaimed movies, including the classic 1974 noir thriller 'Chinatown' starring Jack Nicholson and Faye Dunaway, has died. He was 89 years old. The news was confirmed by Towne’s publicist Carri McClure, who said he died on Monday 'peacefully at home surrounded by his loving family.' No cause of death was provided. Towne won the Academy Award for best original screenplay for 'Chinatown,' which last month celebrated 50 years since being released." |
Related imagery . . .
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Friday, June 21, 2024
Wednesday, May 1, 2024
What a difference an “e” makes.
Auster: The Music of Chance.
Austere: Iacta Est.
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Saturday, February 10, 2024
Gilded Cage Meets Crimson Abyss
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Sunday, December 17, 2023
Sternwürfel 101 — “A Full Course of Instruction”
See also . . .
https://writing.upenn.edu/epc/authors/joris/todtnauberg.html
and Sternwürfel in this journal.
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Wednesday, December 13, 2023
Director’s Exit
For St. Lucy's Day . . . Vide another post now tagged "Cube School."
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Chaos and Boundaries
Another approach to chaos within boundaries: The I Ching —
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Sunday, December 10, 2023
Wrestling
This afternoon's New York Times requiem by Ari L. Goldman for
"a scholar who wrestled with the interplay of tradition and modernity"
suggests a link to another such scholar I personally find more interesting . . .
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Erin’s Barron’s: Skye High
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Sunday, December 3, 2023
Red Skull and the Tesseract Box
Related art by Basquiat —
Click on the above image for an Instagram description of its source.
See also related artistic remarks in this journal on the date of that
Instagram description — October 17, 2022.
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