913.00 A Quanta Module

913.01 The A Quanta Module is \sfrac{1}{6}th of a Quarter-Tetrahedron. The six asymmetrical components of the Quarter-Tetrahedron each have a volume of $\sfrac
{1}$th of the unit tetrahedron. They are identical in volume and dimension, but three of them are positive and three of them are negative. (See Illus. 913.01.)

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Fig. 913.01 Division of the Quarter-Tetrahedron into Six Parts: A Quanta Module:

1. The regular tetrahedron is divided volumetrically into four identical quarters.

2. The quarter-tetrahedron is divided ino six identical irregular tetrahedra, which appear as three right-hand and three left-hand volumetric units each equal in volume to \sfrac{1}{2}th of the original tetrahedron. This unit is called the A Module.

3. The plane net which will fold into either left or right A modules is shown. Vertex C is at the vertex of the regular tetrahedron. Vertex E is at the center of gravity of the tetrahedron. Vertex D is at the mid-edge of the tetrahedron. Vertex F is at the center of the tetrahedron face. Note that AD = FB, DE = EB, and AC = CF.

1. Positive and Negative: The positive and negative A Quanta Modules (the + and the) will not nest in one another congruently despite identical angles, edges, and faces. The pluses are inside-out minuses, which can be shown by opening three of their six edges and folding the three triangles’ hinged edges in the opposite direction until their edges come together again.

2. The/ Quanta Module triangle is possibly a unique scalene in that neither of its two perpendiculars bisect the edges that they intersect. It has three internal foldables and no “internally contained” triangle. It drops its perpendiculars in such a manner that there are only three external edge increments, which divide the perimeter into six increments of three pairs.