### 'a', 'b' and 't' Modular Units

##### Buckminster Fuller's Most Effective Minimum Modular Units

Sphere Family - 'a'-'b' modules

Bubble Family - 't' modules

The '+'s and '0's that you see are the handedness (spin) of the 'a'/'b' modules. One is the inside-out version of the other. If you start at the top of these images you see 6BB tetras and octas divided in 1/4 and 1/3 divisions. In the middle below them is a coupler, underneath that a 1/8 octa mod. Underneath that is a 1/4 coupler made of 6 'a'/'b' mods. It keeps dividing until we have the two spins of the 'a' and 'b' mods. The composite systems show how the tetra/octa/coupler interconnect with each other. Newtools has developed a mass production technique for build these Most Effective Minimum modular units.

##### Mass Production of 'a' and 'b' Modules

The key to understanding how to build these modules is the green rectangle. When you divide it in half you form a sphere triangle inside. The hard-to-visualize part of these modules comes from dividing the edge of these sphere triangles into 1/3 segments. Divide the rectangle along its diagonal and connect the corners to these 1/3 division. As simple as that.

### One Tetravolume (TV) = 24Q

##### 1 'a' mod = 1/24 TV = 1Q

1 'b' mod = 1/24 TV = 1Q

I am going to make all volume in Newtools geometry relative to the volume of the 6BB equilateral tetrahedron. It takes 12 (0) 'a' mods and 12 (+) 'a' mods to construct that tetra. I will call these 1/24th TV mods 1 quantum of volume (Q). 24 Q = 1 TV. Each (Q) connects the center of the tetra to the outside corner, midpoint and center of triangle. We can now catalog the other volumes relative to this minimum.

##### 24 'a' Modules Built 6BB Tetrahedron

##### Looks Can Be Deceiving

3 types of 1 Tetravolume

When you look at these three structures they do not look like they all share 1 TV (tetra volume). Fuller's synergetic volume system of 'a' and 'b' mods lets us count the volume to confirm. Above is proof that 12(0) and 12(+) 'a' mods build the 6BB tetrahedron.

##### 1/4 6BB Octahedron Volume = 1 TV

6BB Octahedron Volume = 4 TVs

6 (0) 'b' mods

6 (+) 'b' mods

6 (0) 'a' mods

6 (+) 'a' mods

24 Q = 1 TV

##### Coupler

4 (0) 'b' mods

4 (+) 'b' mods

8 (0) 'a' mods

8(+) 'a' mods

24 Q = 1 TV

##### Inside Octa, Tetra and Coupler

We start with a 6BB VE's hexagon equator placing 'a' mods to build the tetras and 1/2 octas. The next imagine adds 'b' mods on top of the 'a' mods to begin to build the 1/2 octas. This is the fundamental relationship between 'a' and 'b' mods.

The 6BB VE is made up of 8 6BB tetras and 6 1/2 6BB octas. The tetras are made of only 'a' mods while the 1/2 octas are a combination of 'a' an 'b' mods.

##### Sphere Family TV Volumes

### Bubble Family 't' Modules

We discover the 'a'/'b' mods are only for the Sphere family. The Bubble family's volume is defined by what Fuller called the 't' mod. I have not found the conversion constant between these two volume systems.

The 't' mod begins with a square whose edge is the addition of the 1/2 long, 1/2 short axis of the triaconta's bubble diamond. This is a numerical and structural constant. We will find that you can slice the 't' mod to accommodate the other systems in the Bubble family. Shown here are the internal divisions of the square with the altitudes of the icosa and dodeca defining the two lengths. These are the lines where you can slice the 't' mod for the different systems.

The first module taken off reveals the icosa/dodeca combination. The next one defines the icosa. The next reveals the dodeca and finally the icosidodeca.

Newtools geometry defines, measures, maps and builds physical models of the communication networks that exist between the centers of fundamental structures and the locations-in-common on their outside limits. My theory states our You/Me Ball 'remembers' the 14 directions-in-common between the Sphere and Bubble families (8 blue, 6 green) and the 2 different 12 around directions of these families; the 12 white directions of the Sphere and the 12 red directions of the Bubble. This information gives us a 'push-off-start' to understand modular units like the 't' mod.

The 't' mod connects the center to the 5 outside limits of the bubble diamond, 2 red directions, 2 blue directions and the green direction in the center. To accommodate the other systems begin to slice off part of the 't' mod.