Planar Close Packing-2

Troy R. Bishop noticed my August 6, 2006 Star of David posting about his article, "Starring the Circle," and Planar Close Packing and wrote to me:

I thought you might enjoy my view of the Star of David as a two-dimensional representation of what is really a three-dimensional reality.

 I have prepared and attached a short (9-page) excerpt from my book, "The Multilevelate Universe," currently available at amazon.com.  The front portion of the material is not going to be of interest to you, since it uses terms and concepts that have been developed earlier in the full book and will be puzzling without the earlier portions.  But the final paragraph or two and the illustrations that apply to it might interest you.

So here’s the final paragraphs:

 See how the visible and hidden lines of the cubical outline, taking on seemingly

unaccustomed turnings, are really the versal hexagon (hence

the versal disk). The versal hexagon, we see in this new perspective,

is the versal cube seen along the structatal cubal diagonal, the

perception of depth along the line-of-sight being lost because of the

The Diamond Ladder

orientation of the observer and compressed into the planarity of the

versal hexagon.

In the versal cube, the Star-of-David pattern of the versal hexagon

is seen, released from its two-dimensional bondage, viewed

in the clarity of three dimensions. It is in reality two structures

mistaken as one: the separate, parallel versal sheets observed, like

two celestial constellations, from a direction that causes them to

appear to lie in the same plane. The origin—the one unidentified

bead—of the versal cube is the synthoton of the multilevelate triate,

the unonic needle’s eye from—or through—which the versate blossoms

into being.

And here is one of Troy R. Bishop's illustrations: