If point P exists, there would be 4 planar faces, P1...P4.
According to the link:

https://blender.stackexchange.com/questions/46113/how-to-make-all-quads-or-ngons-on-your-mesh-planar-2d

"when a vertex has more than 3 surrounding faces, their planar intersection does not necessarily exist - it would be actually very rate if it did:"

- Brian

But we have intuition that is maybe possible! :)

Point

Sorry i can't Planar this one in your file!

I think it's not possible with your file.

P1, P2, P3, P4 are defined by 3pts for each as all planes 3 points define a plane.
P1 (A, B, H)
P2 (B, C, D)
P3 (D, E, F)
P4 (F, G, H)


The question is : does exist a point P which is on P1, P2, P3 and P4 ?

I think, we have two possibilities to determine it :

1/ Mathematical with a system of equations (each plane is determined by a equation) and its resolution.

2/ MOI (or CAD drawing)
if we do planes P1, P2, P3 and P4 with points A,B,C,D,E,F,G,H with their 3 points, we can do intersections of these 4 planes. If we have only a point... we win and have P !
With your file, the result is a small thetahedron... P does not exist.

My analysis. right or wrong ?

I suppose yes because all edges A to H are "rigid" and that limits variation but in some cases we can make it...

I am waiting answer from a guy who has found a solution but i believe there is an artefact!

@ Rudl

With your file i can make it if i Up "E" on "Z" vertical by 0.05 unity! ;)
I will verify if i obtain the same with the original...



Ok I obtain the same result with the original... 0.05 unity :)

Maybe this distance can be reduced by taking another orientation than the Z vertical line?...

In any case for the moment this point P seems impossible with this given structure!

@Phiro
You seems right...the answer that i was waiting confirm your...there was a similar construction like mine above...

Point P with this structure seems not possible...very tiny but not..we must move slightly point E !
(so some others not shown here) :)

Similar project with same workflow for a dome I did a while back.
I used RHINO UNROLL Command to flatten all faces.

3D world is a small planet! ;)

We have to be allowed to dice it up into more than 4 surfaces....

Ah that is a brilliant answer! Bravo...

You have the original structure Yes!
You fill the hole Yes!
You have only planes Yes!
You have not 4 planes but 8 so better twice! :)
And you have only quads Yes!

And there is an infinity of this solution! Excellent!
Burmann's Triangles wins ! ;) Bermuda Triangle ? :)

In situ



More flat


Complete



Now the best will be a little script or Elephant for automatise the down levels
or maybe a tricky use of existing functions (Loft, Sweep, NetWork...) for have directly plane surfaces from false surfaces! (dream :)
I have seen during this little exercise than NetWork has numerous parameters! (Uniform with number of Points...)

By hands it's 20 seconds for the last 4 top quads ;)

For this : here by hands its nothing for 12 quads but when you have 200-300 it's another story :)

It's true Quads "plane" built by external perimeter!


Not like that but...

Ultima days of summer! :)

Found a little trick...

Give a constant base angle...and so possibility to put any length to the segments
so not marvelous but..all faces are now planes! :)
https://moiscript.weebly.com/uploads/3/9/3/8/3938813/last_in_translation.3dm

All blue faces are planar!
Constant angle by row...red faces are not planes! Angle not constant on the red original surface!






Taking the same length for the segment than the red structure...but as the angle is constant by rows... at the end some is missing at the right side! :)


Right side faces are a little deformed but now all yellow volume is quasi wraped!

Hi Pilou,

I am trying to make all faces on this structure coplanar as some are no trying to follow your process but how did you insert the intersecting lines from the junction points.




thanks
Alex.

You have different methods

Here is this one with the losanges...
one by one
Scale 3D the losange from center for overpass the 4 segment
Intersect (Trim) the verticals (or oriented, Normal etc..) with the 4 segments around the losange
PolyLine the 4 points



then...

With your 4 facets (FlowExtend Srf ? Very cool! )
https://moi3d.com/forum/index.php?webtag=MOI&msg=9747.21

Make boolean like this

Select 1 2 Call Boolean Isect 3 4 as "second object set"
(you can of course take more facets in a pass - in your case 7 vertical Quads selection)
that gives the 4 points for PolyLines then Planar...erase not wanted ...etc
But it's an hard work because only "manual"! ;)

For more easy use
Copy Move facets and then process else all will be a mess above the original! ;)
And be more precise than me on these speedy test! (top facet is not well aligned on the b corner! :)

You can ask "Show points" on the result of the Boolean operation!



and ask the native function by Press TAB and write ShrinkTrimmedSrf or make a shortcut
if you don' twant to see big larger of points ;) (maybe that lost some history (?) )

But not sure that is a good thing : more little mess than other! :)

Hi Pilou,
Thanks for link for FLOW EXTEND SCRIPT another great script - I am trying to add the outer boundary 4 points as in your model whats the best process to add those are they just drawn upwards towards Z or are they aligned to the planes in that section.

Thanks again.

These segments can be many things!
Normal to the center of losange then move in their 4 places for intersection with the future growing plane from the losange
Vertical Z...
Inclined to a groundbase for be aligned at something...
etc...
all this will give slightly different results for your Plane following that you want ...

thanks again Pilou a manual process but logical will let you know how the project transpires hoping to make each panel a bolted together plate of steel.