i will add this bit of information here:
Quoted:
" The cube, which is at the basis of our present-day construction methods and of the x-y-z Cartesian co-ordinate system, is not in and by itself a stable configuration. Eight spheres forming a cube are inherently unstable. To gain stability, they must be artificially stabilised by interconnecting them in the way the tetrahedron is connected. In this way, two tetrahedra of four spheres each, joined at their respective centers, form one cube of eight spheres.
It happens that this geometry, as developed by Fuller, is in perfect accord with how crystals grow in their various forms, and that its application in engineering reveals to us the possibility of very efficient structures in terms of economy of raw materials and strength of the resulting construction.
Now how could the discoveries of Fuller be utilised to form a co-ordinate system and why should we venture to do such a task, seeing that the Cartesian x-y-z co-ordinates have done perfect (or almost perfect) service for such a long time?
For one, Cartesian co-ordinates may be a convenient mathematical construct, but they do not accord with nature's ways any more than modern chemistry will ever be able to duplicate the conditions of living organisms.
If we utilise x-y-z co-ordinates not for orientation in a known enclosed space (such as did Descartes), but in space with unknown extension, if our system of three axes in other words does not form one of the corners of a known space, but the point of origin of space extending in all directions, the original three axes are no longer sufficient for orientation. We must double the system, adding a mirror image of the three axes, to be able to describe the space 'on the other side of the corner' (fig. 2).
Normally we do not think of this action as a doubling of the axes, as we simply assign negative values to one of the sides, and positive values to the other. But rigorously, we now have six axes: plus x and minus x, plus y and minus y, as well as plus z and minus z. The fact that the plus and minus parts of each axis seem like one continuous axis does not justify considering them to be one. In fact, for the purpose of orientation, we must specify whether we are locating something on the plus axis or on the minus axis, even if we chose to do so by considering positive numbers to belong to the plus axis and negative ones to the minus axis. So we have, in actual fact, six axes to consider and in order to locate an object in space, we must define its position in relation to three out of six axes.
This is where Fuller's synergetic geometry suggests a way of simplifying our task enormously. If we decide to reduce the number of axes from six to four, taking the basic and most simple stable geometric figure, the tetrahedron, as our point of reference, we may locate any point in space by defining its position with regard to three out of four (not three out of six!) axes of reference. The four axes of reference in this system of co-ordinates are the axes that originate at each one of the vertices of the tetrahedron, intersecting at its midpoint and passing through the middle of each one of the triangles opposite these vertexes (fig. 3). These axes are co-ordinated with angles of 109 degrees, 28 minutes. The four of them represent the minimum set of reference axes emanating from a common origin needed for defining all possible directions in physical space.
I have developed, in order to make this concept more clear and to allow its application as a tool for instant and intuitive orientation in space, a colour coding system that combines these tetrahedron-based space co-ordinates with the currently widely used method of colour separation for printing purposes, the so-called CMYK colour separation process.
CMYK (cyan-magenta-yellow-black) are the four colours used by present day printing presses. The combination of these four colours in various percentages creates a large number of different colours in almost endless continuous shading. Assigning one of the basic colours to each one of the four axes of the tetrahedron, and blending them towards the other axes, we obtain in fact a unique colour for each one of the thousands or millions of possible directions that we may want to instantly identify. Naturally we can also express direction in terms of degrees, minutes and seconds of arc in relation to the three nearest axes.
A part of this article is a printed version of a tetrahedron to be cut out and pasted together, which will beautifully illustrate the principle.
A co-ordinate system of this kind, suitably developed and refined, may be used with profit in astronomy, in navigation (especially space navigation), in holographic representation of images, in crystal-based electronic information storage and possibly a whole range of other, yet-to-be-thought-of activities.
By its use, we transform our four directions of orientation on earth (east-west-north-south) into four directions of orientation in space. We need to develop and use this tool if we are seriously considering to expand our influence into planetary or interstellar space, not only in the sense of observation, but also of exploration and navigation"
end quoted
from:
http://www.hasslberger.com/phy/phy_6.htm
and Time Travel!!!
