Thanks to David, I got clear on three things:
The volume 4 octa in which an icosa is inscribed, faces flush, is the same model Fuller employs to develop his S modules, 24 of which form as the difference between this octa and its icosa. These S mods have a volume close to that of the A, B & T: about 1.08x bigger. Ergo, octa 4 minus x > 1 = 3+ volume of the icosa (where x = 24 S).
The relation between the T & E is a buried gap in Synergetics 2, a 0.9994... that seems too much of a focus (over-amplified?). In 2011, we see E amplified by Phi**3 (volume-wise) giving E3, 120 of which make "super RT", embedded in which, as long face diagonals, is our "most important icosa" (the one from the Jitterbug) with edges 2R. On the T side, we see T amplified by 1.5 (volume-wise) giving K (1.5 T), 120 of which make the 7.5 volumed RT (interlaces with 6.0 volumed RD). The scale factor (volume-wise) to the E3 (E-mod * phi **3) is just 2nd-root(2) ** 3 (linearly: 2nd-root(2)).
The octa scaled up so as to contain the "most important icosa" also embeds a cubocta of edges 1/2 those of the octa. For comparison, the octa 4 (mentioned above) contains the cubocta of volume 2.5. The "most important icosa" is related to the cubocta of volume 20 by Jitterbug Transformation. Interesting factoid: the edge of the cubocta in scaled up octa is 1/10 the volume of the most important icosahedron, looking at PV = 2 (1 D), and icosa-volume = 18.51... with cubocta's edges 1.851... (same digits). That's weird, because we're talking about an edge vs. a volume.
:: opdx 11-10-11 ::
