See Eightfold Froebel.

From this journal —

See (for instance) Sacred Order, July 18, 2006 —

From a novel published July 26, 2016, and reviewed
in yesterday's (print) New York Times Book Review —

See also Log24 on the publication date of Dark Matter .

Click to enlarge:

For the hypercube as a vector space over the two-element field GF(2),
see a search in this journal for Hypercube + Vector + Space .

For connections with the related symplectic geometry, see Symplectic
in this journal and Notes on Groups and Geometry, 1978-1986.

For the above 1976 hypercube (or tesseract ), see "Diamond Theory,"
by Steven H. Cullinane, Computer Graphics and Art , Vol. 2, No. 1,
Feb. 1977, pp. 5-7.

(Continued)

For Pete Rustan, space recon expert, who died on June 28—

(Click to enlarge.)

See also Galois vs. Rubik and Group Theory Template.

Click images for further details.

See also Crimson Tide, Rubik, and Cuber.

For another monochromatic enigma without
guaranteed equality of results, see
Finite Geometry of the Square and Cube.

The hypercube has 192 rotational symmetries.
Its full symmetry group, including reflections,
is of order 384.

See (for instance) Coxeter—

Related material—

The rotational symmetry groups of the Platonic solids
(from April 25, 2011)—

— and the figure in yesterday evening's post on the hypercube—

(Animation source: MIQEL.com)

Clearly hypercube rotations of this sort carry any
of the eight 3D subcubes to the central subcube
of a central projection of the hypercube—

The 24 rotational symmeties of that subcube induce
24 rigid rotations of the entire hypercube. Hence,
as in the logic of the Platonic symmetry groups
illustrated above, the hypercube has 8 × 24 = 192
rotational symmetries.

The New York Times  has a skateboarder obit with a URL date of July 9.

Here is an earlier version from the LA Times—

July 4, 2011

By Keith Thursby, Los Angeles Times

Chris Cahill, one of the original Dogtown Z-Boys
who brought seismic changes to skateboarding
with their style and attitude, has died. He was 54.

Cahill was found June 24 at his Los Angeles home,
said Larry Dietz of the Los Angeles County
coroner's office. A cause of death has not been
determined and tests are ongoing, Dietz said.

More…

Related material from Midsummer Day, June 24, the day Cahill was found dead—

The Gleaming and The Cube.

    An illustration from the latter—

    The above was adapted from a 1996 cover—

 Vintage Books, July 1996. Cover: Evan Gaffney.

For the significance of the flames,
see PyrE in the book. For the significance
of the cube in the altered cover, see
The 2×2×2 Cube and The Diamond Archetype.

A search for “Chinese Cube” (based on the the previous entry’s title) reveals the existence of a most interesting character, who…

“… has attempted in his books to produce a Science and Art of Reasoning using the simplest of the Platonic solids, the Cube. [His] model also parallels, in some ways, the Cube of Space constructed from the Sepher Yetzirah’s attributions for the Hebrew letters and their direction. [He] elucidated his theories at great length….”

— More…

For related remarks, see the link to Solomon’s Cube from the previous entry.

Then of course there is…

Click on figure for details.