Friday, May 28, 2010

Interlacing Test Pattern

Earlier in this blog, the CSN team celebrated the addition of the 7.5 volumed rhombic triacontahedron (RT) to our little zoo of inter-transforming polyhedra.

Most of our polyhedra are isotoxal, to find an arcane term for ya. Any edge may be transformed into any other by a series of rotations.

The 7.5 RT is measured as such relative to a tetrahedron of edges 2, representing the 2 unit radii of spheres in a closest packing arrangement.

The yellow rhombic dodecahedron (RD) depicted above, of volume 6, may serve as a casement for one of these spheres.

Its green face diagonals define an octahedron of volume 4, while its blue short face diagonals define a cube of volume 3.

The outermost cube, in consisting of 8x the inner cube, has a volume of 24 and is what we call the 2-frequency cube in Synergetics.

Synergetics, a philosophy (sometimes categorized as Neoplatonic), is a source for many of our streaming spatial geometry animations.

The above graphic was developed by David Koski using vZome, a virtual version of Zome.

As of 2010, we had few commercial outlets for these streaming mathcasts.

The powers that be were (on average) slow to relay this new kind of philanthropic programming through their networks, to hungry scholars around the world.

Two other RTs you might easily encounter in perusing our mathcasts: the RT of volume 5, with radius 0.9995, so very close to unit radius; the RT of volume 15 * root2(2), with edges 2.

Again, don't expect to find these volume numbers in any 2010 textbook. Tetravolume accounting has not been accepted by the mainstream. CSN traffics in esoterica, simply by virtue of the radical nature of its principal sources of content.