4 corners of the world = spherical tetrahedron (arc'd tet)
not cubic or square flatland.

[[ http://www.rwgrayprojects.com/synergetics/s10/p5300.html]]
Minimum required: 6 restraints (structure) = 6 tet edges (linear or curvilinear ie arc'd)
1 tet + 1 upsidedown tet, interpenetrated, = duo-tet (Stela octangula ie stellated octahedron)
1 tet models a static sphere, (omnidirectional, no equator), compression = tension
1 duo-tet models a rotating planet (unidirectional, equator = internal octahedron circumferance).
(gravity.spin = density.spin)

Planet Earth functions as an arc'd duo-tet (standing wave) with two tropical belts (Capricorn, Cancer) as the outermost boundaries of the equatropical realm where hurricanes-typhoons-cyclones flourish (flux in pressure zones). Planetary pressure zones are equivalent to the spinning tet "corners", invisible like the wind but present and visible to weather satelites via clouds.

Earth.nonspin = arc'd tet (nonrotating, nonpolar "solid" sphere)
Earth.spin = arc'd duo-tet (rotating "solid" sphere, North pole & South Pole)

Where tet 1 models physical mass (particle sphere), its dual, tet 2 (inverted 180 deg.) is "non-physical" energy (waves), the intersection of these interpenetrating tets (an arc'd octahedral "solid" radioactive nuclear core),
the union of these interpenetrating tets (an arc'd duo-tet (standing wave model) of geophysical liquid-solid globe),
when surrounded by a gaseus low viscosity/friction fluid atmospheric (cuboctahedral-icosahedral flux state (jitterbug ala RBF)) shell(s) constantly absorbing, reflecting and diffusing external (solar) energy, modelling the earth in rotation and orbital cycles.

Planets must spin, they are round due to simultaneous erosion (like streamside pebbles), accretion (accumulation of dust), chemical-physical bond exchange (from omnidirectional to unidirectional). "Spherical" planets are not polyhedral, since they have no flat sides, however if sides = vectors between adjacent particles then they can be triangulated and thus become polyhedral.

Re: Infinite dimensions (from Synergeo yahoo group)

JBrawley: If you're going to "arc" a tet into a sphere, then I suppose you can "arc" _any_ convex polyhedron into a sphere....

DDeden: Since any polygon can be reduced to a discrete number of triangles, and any polyhedron (or polychoron) can be reduced to a discrete number of tets, there is no need to arc other polyhedrons into spheres, though of course it can be done.

Synergetics uses a tet for 4D, Synarctics uses a sphere for infinite D

TStockton: Just understand the first 10 before you talk about infinity.

DDeden: Once you start counting dimensions ("first 10"), you've created another one (complexity). In the same way, the first dictionary did not contain the word "dictionary". Bucky's "Synergetics" went with tets as the simplest structure in Universe, this fits with Synarctics, since a sphere is an arc'd tet. A stable spinning (apparently oblate spheric) planet OTOH is an arc'd duo-tet.

Since a sphere can be understood as an arc'd tet, Synarctics and Synergetics are commensurable, and supplementable.

To be continued... mental meandering through interdimensional imagery