The Octahedron, Tetrahedron and Cube (Hexahedron) combined in the OTC pyramid truss unit

We begin with the Tetrahedron.
It is the 'lowest common denominator' of structural systems.
As part of our design, mid-edges have a Connector Hub for adding the dual-opposite Tetrahedron:

Dual Tetrahedrons form the vertices of the Cube and basis for the design of our "Tetra-Dome":

Tetrahedron mid-edge points also define the vertices of the Octahedron:

The Tetra Duals and the Octa:

Tetrahedron points are joined to make the Cube:

The Tetra Duals get a translucent covering:

Part 2