An Integral Closed Astralit is best defined by breaking down its three component parts. An Astralit is any connected series of consecutive faces which are related to one another by simple or primary tropes (Major & minor Deo & Wid). An Integral Astralit is one where these tropes or turns pass through each of the 24 exact faces in one consecutive series without duplication. An Integral Closed Astralit then is a consecutive trope series arranged such that when the passage through all 24 exact faces on the tablock arrives at its 24th position, it is is returned to the 1st (or idemfactor) face by a simple turn; thus connecting the series from beginning to end.

One basic example of an Integral Closed Astralit is demonstrated by moving the male tablock through its numbered positions beginning with Upright Y (1357) and turning sequentially through each of the faces as numbered, e.g. 1,2,3,4,5,6....24,1.

This Integral Closed Astralit series can also be outlined in a table, which is called a Rational Cradle:

An Integral Closed Astralit may begin with any of the 24 exact faces for either the Convex or Concave tablock. The corresponding 48 rational cradles that are constructed from these instances may be assembled according to a set of governing rules, or by empirically observing the tablock while rolling through its prescribed series of turns. As an example, beginning with Upright A Vex (4321) the tablock postures will be 3, 22, 23, 6, .... 24, 1, 2, 3 as illustrated below:

This particular Integral Closed Astralit is tabulated in a rational cradle below. Note the postures for each exact face are indexed:

Close study will demonstrate that there is a certain uniformity to posture sequences for the Male & Female sides of these rational cradles. You will also note that the specific turn which joins the end of the male to start of the female side of a rational cradle is the same type of turn which brings the end of the female side back to its starting male face in the cradle; thus closing the sequence.

Again, the results should be checked against the physical tablocks to verify correctness between thought & action. Alternately, the virtual tablocks may be used for online reference, but it is recommended that a proper physical set of tablocks be created for study since the consecutive turns will be more smoothly & easily done by hand.

NEXT