Hi to you 3 – Alain – mikeh & SteveM.

It's really fun to see you both trying to beat a dead horse (Alain's diagram) over the finishing line of your fantasies ...

… and there is nothing wrong with having dreams – but when Alain claims that his diagram is based on the TETRAKTYS …

https://en.wikipedia.org/wiki/Tetractys
… it has to fit the bill of 10 dots arranged in that specific fashion.

Otherwise it won't be based on the TETRAKTYS …

… like I've pointed (pun intended of course) out already …

viewtopic.php?f=11&t=1102#p16920
… there CAN NOT BE a model that is based on the TETRAKTYS that has 78 dots for obvious reasons.

By addition only it can be demonstrated that 80 dots with 8 similar shaped TETRAKTYS elements MUST be the stock for such a model.

So there is a very simple explanation WHY it was so …

… notoriously difficult to put the cards of the tarot sequence into groups that actually have something in common …

… and you have obviously not thought about that because you were so busy to collaborate for your dream come true.

The explanation is that the diagram Alain made up is indeed …

… a hodgepodge …

because TESSELLATION has the following RULES …

A tessellation is a repeated series of geometric shapes that covers a surface with no gaps or overlapping of the shapes. This type of seamless texture is sometimes referred to as tiling. Tessellations are used in works of art, fabric patterns or to teach abstract mathematical concepts, such as symmetry. Although tessellations can be made from a variety of different shapes, there are basic rules that apply to all regular and semi-regular tessellation patterns.

Regular Polygons

All regular tessellations must be made of regular polygons. Polygons are geometric shapes made of straight sides connected sides. A regular polygon is a shape comprised of sides that meet to form angles that are all equal, such as a square or an equilateral triangle. However, not all regular polygons can be used to create a tessellation because their sides do not line up evenly. A pentagon is an example of a regular polygon that cannot be used to tessellate.

Gaps and Overlapping

Tessellations cannot have any gaps between shapes or overlapping shapes. Regular tessellations must have sides that match and fit together entirely, such as when you put two squares side-by-side. As mentioned previously, not all regular polygons can be used to create a tessellation because there are gaps between them when you place two side by side.

Common Vertex

All regular polygons that meet must have a common 360 degree vertex in order to be used in a tessellation. A vertex is a point where two sides come together to form an angle. For example, in an equilateral triangle, two sides come together to form a 60 degree angle. In a tessellation, a vertex refers to the point where three or more shapes come together to equal 360 degrees. For example, three hexagons, whose interior angles equal 120 degrees, come together to form a vertex of 360 degrees, while a pentagon, whose interior angles measure 108 degrees cannot equal a vertex of 360 degrees.

Symmetry

Polygons used in a tessellation must have at least one line of symmetry. Symmetry can be defined as equal parts facing each other around an axis, sometimes referred to as a mirror image. Because regular tessellations are created by repeated polygons, a tessellated figure can be divided evenly down the middle, from various angles, to create two symmetrical shapes on either side of the dividing line. Regular tessellations should have multiple lines of symmetry.

http://www.ehow.com/info_8736965_rules- ... tions.html

The site offers also tutorials for making your own TESSELLATIONs.

Maybe you should have a look BEFORE your next collaboration in this clearly defined field of GEOMETRY.

Now you are right instead here when you claim that …

… Most of it was easy to follow …

… because that's the defining streak of POPULISM (in this case not right or left winged – but TAROT colored & seemingly ignorant about the roots of problems).

Alain made up a model of 78 dots situated in an rectangular triangle and grouped those dots according to his liking to fit his TAROT idea of several defined groups. And his trick(or MISTAKE) was to IGNORE the SHAPES which must follow the TESSELLATION RULES. So making only dots and NO shapes to cover the dots of every each group and joining these grouped dots with a line created the ILLUSION that there is TESSELLATION when in reality there is NONE

By definition the RULES for TETRAKTYS & TESSELLATION are not met.

So the diagram as a model based on these principles is REFUTED in totality.

He could instead leave OUT these terms TETRAKTYS & TESSELLATION – and all would be totally OK!

But NOBODY would CARE about such a diagram – am I right?

YES I AM.

And now you can IGNORE this again – like you did before – and hide this TRUTH behind some other WALL of meaningless details (and NAMES!) that can NOT be applied to this already DEAD horse.

This is putting a nice and precious bridle on the dead horse after it came back from the taxidermist and presenting it to the press as the winner.

In real life this would be FRAUD.

What is such called in your TAROT world?

Adrian