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From: Clifford J. Nelson on 12 Oct 2009 01:22
They will, and probably should, delete the Wikipedia article about Synergetics coordinates.

http://en.wikipedia.org/wiki/Synergetics_coordinates

The n Synergetics coordinates axes are perpendicular to the n defining geometric objects that define a regular simplex; 2 end points for line segments, 3 lines for triangles, 4 planes for tetrahedrons etc.. The angels between the directions of the coordinate axes are Arc Cosine (-1/(n-1)). The coordinates can be positive or negative or zero and so can their sum. The sum of the n coordinates is the edge length of the regular simplex defined by moving the n geometric objects in increments of the height of the n-1 dimensional regular simplex that has an edge length of one. If the sum of the n coordinates is negative the triangle (n = 3) or tetrahedron (n = 4) is upside down and inside out.

The above is implied by closest packing of equal diameter spheres and:

See Sections:
Figure 465.01
527.711
527.712
966.20
966.21
962.04
962.03
And footnote 4 of 986.222.
From Synergetics by R. Buckminster Fuller at:
http://www.rwgrayprojects.com/synergetics/synergetics.html

Cliff Nelson

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