(more coming)

In Topology, a "network" is a series of points connected by lines ('line segments').
A "vertex" is a point with lines attached.
A vertex's "order" is the number of lines which terminate upon or originate at a point.

There are several different sorts of networks, among which are "complete" networks--those in which every point is attached by at least one line segment, to every other point. Tetrahedraverse is NOT a "complete" network.

Thus, a Network of Vertex order 12 is a set of points, all of which have twelve line segments attached.

In two dimensions, this is probably impossible.

In a three-dimensional network, in which linesegments are more or less the same length, this equates to a set of points all of which have twelve and only twelve neighbors. You will recognize this as a network in which every 13-point region looks like an icosahedron--albeit an IRregular icosahedron.

"Higher dimensions" —geometrically speaking— are irrelevant to Tverse; they don't exist.

A CCP (Fuller's favorite; Kepler's Conjecture; Hales and Ferguson's 'proof'ed) is a vertex order twelve network. Tetrahedraverse's most likely internal arrangement is also a vertex order twelve network, but one cannot be certain that it is 100% so; there are some peculiar things about it that, were you to study it, you might find, as I have.

But, find all that stuff elsewhere on the site, please; this page is for defining what that particular network is. Details elsewhere.