Thursday, June 25, 2015

sFactor (Svol / Evol)

Talking geometry, with S and E two tetrahedral slivers, close in volume but Svol > Evol, such that Svol / Evol > 1.  sFactor = 1.080363026951 (rounded).

Scaling the Icosahedron by sFactor gives the corresponding Cuboctahedron volume, as if Jitterbugged.

Scaling twice more gives the Icosahedron said Cuboctahedron was "skew to" i.e. a different relationship from Jitterbugging, faces flush but only partially overlapping.

Going the other way, the 2.5 (exact) cubocta becomes the 2.918 (rounded) icosa, likewise inscribed in (eight faces flush with) the volume 4 octa.

Fig. 988.00 Polyhedral Evolution: S Quanta Module:
Comparisons of skew polyhedra.

Applied again, and we Jitterbug.  18.51 -> 20.

Two to twist, one to leap, something like that ("applications of sFactor" being the multiplied verb).

For more details:  click here

Thursday, June 11, 2015