T-module as 120th of Rhombic Triacontahedron
The Rhombic Triacontahedron is the polyhedron from which the T-module is first identified. Thirty rhombic faces make up the surfaces of the Rhombic Triacontahedron. These thirty faces correspond to the edges of the two most commonly know five-fold polyhedra, the Icosahedron and the Pentagonal Dodecahedron. These two polyhedra are duals of each other, in that, by itemizing the faces, points and edges and plugging them into Euler’s characteristic, we get:
Icosahedron= 20 faces + 12 points = 30 edges + 2
Pentagonal Dodecahedron= 12 faces + 20 points = 30 edges + 2
Note that the faces and points have been reversed. In the Rhombic Triacontahedron the long diagonals in any rhombus correspond to the edges of the icosahedron and the shorter to the Pentagonal Dodecahedron. They cross at their mid-points. One fourth of one of the thirty rhombi is 120th of the surface, which R Buckminster Fuller called the LCD (lowest common denominator) triangle. By projecting the three points of this triangle to the center of the Rhombic Triacontahedron we get the T-module. Bear in mind that there is a “left and right handed” version of the T-module, so 60 left and 60 right handed T-modules add up to the 120 total.
