If the mesh “closes up”, so that the skews come into contact,
the tetrahedral cells,
and the hyperboloid nature of the whole construction,
must collapse (degenerate) into a single line.
To see this happen, drag one of the white circles
near the bottom of the figure towards the other.
The skews will approach each other.
(In this case, they all approach
one and the same line, like the chords of the
first possibility considered in ‘On Limits’
and for much the same reason .)
one and the same line, like the chords of the
first possibility considered in ‘On Limits’
and for much the same reason .)
When they finally touch, the ‘apparent’ flanking hyperbola
will have degenerated
into two lines through a vertex .
This is a conic section.
So, just as long as it is ‘hyperboloidal’, this structure must have
an irreducibly-discrete, tetrahedral, cellular “grain”.
It is a Net of Tetrahedral Cells.
A ‘skeletal’ version.
(Imagine you are flying around a stationary wire frame.)
