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Synergetics coordinates from a tetrahedron

  • To: mathgroup at
  • Subject: [mg57697] Synergetics coordinates from a tetrahedron
  • From: "Clifford J. Nelson" <cjnelson9 at>
  • Date: Sat, 4 Jun 2005 03:04:45 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

You could make a coordinate system from the whole to the parts, based on 
the closest packing of spheres, instead of building up from axioms or 
reference vectors: rack up a triangle of pool balls on a pool table and 
put a smaller triangle of balls on top of the big triangle of balls and 
then a smaller triangle on that one, etc., to make a tetrahedron of pool 
balls with five balls on each of the six edges, thirty five balls 
altogether. Bisect the edges by removing pool balls to make an 
octahedron and bisect the edges of the octahedron to make a 
cuboctahedron of thirteen balls. The four planes that defined the 
tetrahedron could move inward one layer of balls and meet at the origin 
of the coordinate system (4D) which is at the center ball of the 
cuboctahedron. Three of the four planes cut the bottom fourth plane if 
the fourth plane doesn't move from the origin to make triangles in the 
plane (3D) and two of the four planes define signed line segments (2D) 
if the other two planes do not move from the origin of the coordinate 
system. Look up closest packing of spheres on Google to see how everyone 
else starts with a coordinate system in mind before they do some packing 
and they are very confusing (CCP, FCC, HCP).

Somebody's got to rack'm up and show the process in graphics on the net 
with nice gleaming spheres and four translucent planes.

I don't know how to show that with Mathematica.

  Cliff Nelson

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"Forward Into The Past" 2 PM to 5 PM, Sundays,
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