🚀 go-pugleaf

pdx4d@teleport.com (Kirby Urner) wrote:

>In my own case, my training in polynomials came in useful 
>when I was trying to derive a formula for the cumulative 
>number of balls in a cuboctahedral packing.  Starting with
>a nuclear ball, you pack 12 around it, each tangent to the 
>central one and 3 neighbors.  
                 ^^^^^^^^^^^

Oops.  That's 4 neighbors.  

You may have seen the related math gizmo, sold in science
museum gift shops and toy stores.  DaMert makes a glow-in-
the-dark version, called 'Vector Flexor' (others have 
called it that too).[1]

The cuboctahedron, an Archimedean polyhedron having 6 
square faces, is structurally unstable (unlike the 3 
omnitriangulated Platonics: tetrahedron, octahedron, 
icosahedron, which are).  As a result, it can be easily
deformed (hence the term 'vector flexor') into numerous
other shapes.

For a better picture of how 12-spheres-around-1 and
the cuboctahedron fit together as concepts, pop this
gorgeous graphic (URL below):

http://www.teleport.com/~pdx4d/images/vesphere.jpg
(by Richard Hawkins, using a Silicon Graphics machine)

Kirby

NOTE:

[1] I do not stand to gain financially by your purchases
of DaMert products, although I did have a hand in writing
the informational booklet that goes with Space Ball, 
a snap-together hexapent (e.g. makes a dynamite glow-in-
the-dark model of buckminsterfullerene).  I was paid a
flat fee by a different company, Mondotronics (which later 
sold the idea to DaMert).

----------------------------------------------------
Kirby Urner  "ALL realities are 'virtual'" -- KU
Email: pdx4d@teleport.com
Web:   http://www.teleport.com/~pdx4d/