In the last post introducing ET Foundations, the simple circularity characterizing support bases for outwardly-projected constructs was defined by the intersection of the geocentric cuboda’s cylindrically enveloped spheres and earth’s surface.
Derived thus, the cylinder is only one of a handful of basic forms spun about central vertical axes that may guide artifacts intended to set upon the circular pads. In fact, much of the same geometry guiding the supported constructs is employed by the pads themselves.
As plainly exhibited by the 3D cross-sections of circular landscaping mounds, waveforms represent the smoothest, most elegant transition from one level to another. As such, a pad supporting ET constructs is basically a mound centered by a flat circular plateau.
Recall that the maximum slopes of mound waveforms are keyed to the sloping elements of the vertex-up cuboda, with particular slopes determined by the role played by the mounds in a greater grid context.
For example, the 30° sloping edge defines the maximum slope of an inter-grid juncture while the 35° sloping triangle defines the slope of an intra-grid juncture.
To some extent, projected mounds may go beyond filling a context role to actually defining the greater context. For example, a 35° max-slope mound might characterize a pad situated along the direction of a grid line defined by the projection of the edge-up cuboda. In such case, the edge-up cuboda’s 19°, 35°, or 60° angles manifest in a configuration of at least 2 concentric rings.
The bottom outer slope represents the greater grid by manifesting either of the edge-up’s sloping planes (19°, 35°) with 19° representing the only use of that angle in a circular mound to in effect distinguish its role as a support pad. The inner waveform either possesses the slope opposing the outer waveform or that of the common 60° edge.
As such the slope either goes up in a terraced fashion or down into a crater setting. In either case, the center portion bearing the ET construct is circular and typically flat.
As with landscaping mounds, the waveforms may be quarter or half, with the waveforms’ defining points – crest, trough, and maximum slope – posing natural transition points for the introduction of cylindrical and truncated conical forms.
By the same dual-ring approach, a hexagonal grid foreign to the rectilinear nature of both the polar-rotational and diamond grids may be introduced. In such case, the 2 orientations are integrated by the universal linking intermediary of the cylinder defining their boundary.
In such case, the inner ring – the upper terrace or crater waveform – would have its maximum slope keyed to the triangle-up cuboda bearing the hexagonal pattern. Those slopes correspond to the 55° square or 71° triangle.
The hexagonal pattern is plainly more circular than the rectilinear pattern for basing a circular cross-sectioned artifact. But as a triangle-up cuboda-guided construct must exist in the P-R and/or diamond grid context, how the triangle-up cuboda relates to the host grid is examined.
First the 8 directions of the alternating grids are transposed on the circle integrating them both in an orthogonal manner. Then a vertically oriented triangle is positioned via primary and secondary rotations in opposing (left/right) senses and the same is done for the horizontally aligned triangles, with 8 points added to the circle.
The same maneuvers are implemented with tertiary rotations about the axes of the diamond grid orientation to add 8 more points. All in all, 16 points are added to the 8 provided by the P-R and diamond grids for a total of 24 separated evenly by 15° – just like the hours of the time zones. As each point partakes of both a square and a triangle, the whole layout constitutes a kind of universal configuration for projected constructs having a circular cross-section.
15-Such sectioning is useful for structuring the support of ET artifacts and is essential to affording access to and through the pads, a major consideration addressed in the next post.