A solitaire element that has an internal – spherical shape forming – mechanism is a true scalar. That means that the scalar is determined by only 1 value – its radius – irrespectively its position in space and time.

There are no solitaire elements in our universe thus every element is a deformed scalar. That is why the invariant volume of every element is divided in:

- a deformed part of the volume (vectorized volume),
- a not deformed part of the volume (decreased scalar).

The result of the existence of the deformed elements is the creation of a composed vector and scalar field. This composed basic field is everywhere in the universe and tessellates space.*figure 4*

The image above shows the scalar part of the elements when all the decreased scalars have the same radius (so it is a flat scalar field). The different colours are used for visibility.

When every element has an identical decreased scalar and an identical vectorized volume the hypothetical symmetrical element shows to be a rhombic dodecahedron. So all the rhombic dodecahedrons together tessellate space. The image below – figure 5 – shows one symmetrical element with the decreased scalar inside.

*figure 5*

The internal spherical shape forming mechanism of the elements is never in equilibrium because every element is a deformed true scalar. The consequence is the continuous alteration of the shape of the elements because the volume of every element is identical and invariant.

*So how do the elements deform?*

The deformation of an invariant volume means that some volume of the element becomes surface area and vice versa. The mechanism behind the deformation of the invariant volume – actually a topological homeomorphism – is showed in figure 6 (cross section of the joint face between 2 rectangular bodies).

*figure 6*

The only way to keep the volume of both bodies constant is to move 2 or 3 blue arrows or green arrows. Thus the sum of the transfer of volume is null.

An element is a deformed true scalar. That is why the alterations of an element are similar. The radius of the inscribed sphere – the undistorted decreased scalar – can only increase or decrease at the points of contact between the scalars of the adjacent elements.*figure 7*

The image above shows the schematic cross section of 2 adjacent elements. The internal spherical shape-forming mechanism is visualised by concentric circles.

It is easy to conclude that alterations by the decreased scalar – actually an internal transfer of volume – can only happen at the contact point between both elements.

*figure 8*

The image above (8) shows the combined basic field. The white spheres are the decreased scalars (scalar field) and the arrows show the alterations at a certain moment between the vectorized parts of the volumes of the elements (only the resulting vectors are drawn).

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