**Solomon's Cube**

**By Steven H. Cullinane on May 28, 2003**

In 1998, the Mathematical Sciences Research Institute at Berkeley
published a book, *The
Eightfold Way*, inspired by a new sculpture at the Institute.
This note describes another sculpture embodying some of the same concepts in a
different guise.

*The Eightfold Way* deals with Klein's quartic, which,
like all non-singular quartic curves, has 28 bitangents.
The relationship of the 28 bitangents to the 27 lines of a "Solomon's seal"
in a cubic surface is sketched at the Mathworld
encyclopedia. For more details, see the excerpt below, from Jeremy
Gray's paper in *The Eightfold Way*.

Both the 28 bitangents and the 27 lines may be represented by the
63 points of *Finite
Projective Spaces of Three Dimensions* (Clarendon Press, Oxford,
1985).

Group actions on the *63* points of the finite
*projective* space *64* points of the finite *affine* space

Those who like to associate mathematical with religious
entities may contemplate the above in the light of the 1931 Charles Williams novel *Many
Dimensions*. Instead of Solomon's *seal*, this book
describes Solomon's *cube.*

From a
review: "Imagine 'Raiders of the Lost Ark' set in 20th-century London, and
then imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture of Charles
Williams's novel *Many Dimensions*."

From *The
Eightfold Way*, a publication of

the Mathematical Sciences Research
Institute

(MSRI Publications Vol. 35, 1998):

**From
the History of a Simple Group**

**by Jeremy
Gray**

Excerpt:** **

"Art isn't easy." -- Stephen Sondheim

For more on this theme, see

**ART WARS: Geometry as Conceptual Art****.**

For a large downloadable folder

containing this and many related
web pages,

see Notes on Finite
Geometry.