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.
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).
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.
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).