[Edu-sig] Signature Building Blocks

[kirby urner]

If there's a signature Fuller polyhedron, it's probably the Coupler:

>>> import syngeom
>>> mypoly = syngeom.Coupler()
>>> mypoly.volume
1
>>> mypoly.isaspacefiller
True

Some immediately object no fair gluing together already known pieces
and *naming* them.  But it's not a priority game, it's a getting work
done game, and we need to call them something or other, so why not
Coupler, since it's already nicely sorted out:

>>> amightyMite = syngeom.Mite()
>>> amightyMite.volume
0.125
>>> amightyMite.modules
[A,-A,-B]
>>> [i.volume for i in amightyMite.modules]
[0.041666666666666664, 0.041666666666666664, 0.041666666666666664]

MITE is an acronym from MInimum TEtrahedron, an irregular tetrahedron
with a 90-90-90 XYZ corner that's able to fill the 8 corners of the
XYZ coordinating apparatus, thereby putting the Coupler center right
at the origin (0,0,0).

However the Coupler is a bit deceptive in that it's really more of an
interface between neighboring rhombic dodecahedra:

>>> ballcase = syngeom.RhDodeca()
>>> ballcase.volume
6

Plus it works to see it as coupling around all three equators in
various ways (the Coupler being an octahedron):

>>> mypoly.faces
8

At my web site:
http://www.grunch.net/synergetics/modules.html

More in my blog:

Half-Coupler:
http://worldgame.blogspot.com/2005/11/half-coupler.html

Coupler:
http://worldgame.blogspot.com/2004/12/more-geometry-of-thinking.html

Kirby