The frames of the Durheim issues Local Post up to Rayon I light blue) are since always the most controversial points of research among the classic Switzerland stamps. One of the first researchers, Adolf Schulze, questioned the printer and manufacturer Carl Durheim in Bern by corresponding with him. His response to proceed at the printing of these stamps and in particular the full frame with cross was partly completely wrong which also influenced and misled the Baron Axel de Reuterskjöld ( together with the banker Paul Mirabeau, who published the most famous handbook about the classic stamps of Switzerland calle “ die Schweizerischen Postmarken“ of 1899). The fading of his memories through old age may have been the cause that Durheim was not only the printer but mainly followed his second, just completely newly emerging profession which was being one of the first photographers in the world.
His work described the studies of reconstruction of the different printing stones,  of which nobody had much knowledge even after 90 years after their date of issue. He especially concentrated his studies on the frames of the crosses.of which we are interested here in those of the yellow Rayons..The problem with this was that we are dealing here with true world rarities, of which only very few existed.It is all the more astonishing that he got hold of – in a few years- quite a few of these yellow Rayons with complete  cross frames and was able to take photos of them to show us.The biggest collectors of his time showed him willingly their treasures to record them photographically for his studies.

The reconstruction of the different printing stones was in those times not finished. This work was finished after his death in 1973 with the handbook of the Rayon II of Ernst Müller ( thank to the financial support of the Philatelic Dealers Federation ).

It has always bothered me for a long time that there were only vague guesses or incomplete information about the effectively known and proven pieces of the yellow Rayon with the framed. Cross. For the last 40 years, I saved every yellow copy I came across in order to find out more about them. 
A big help for this documentation were apart from the sold copies by myself especially extracts of the archives of Dr. Munk and those passing through the most important auction catalogues of the last 100 years including the archives of the Corinphila auction house, which also contained  many  expert certificates with photos of Hunziker and Rellstab.
It took me many months to look through this documentation. It was not at all easy to define the printing stones and the various subgroups by looking solely and merely at a blurred poor photo plates of an old catalogue. You had to leave out a certain number of copies because we know today that they are clearly forgeries. These were often marked with a question mark, although without further clear proof or explanation.

If I list below a certain number which are recorded in our files up to now, I would like to remind you that this list (like any previous lists) we cannot assume that this list is complete. There will be always suddenly another piece coming up, which has not been seen before. If you yourself have any in your collection, we would be very grateful to receive a photo or copy of an expert cert. with photo of each piece, which allows us to update our documentation.
Known Rayon II with complete cross in a frame:
As Dr. Munk already suspected, we know these stamps of both printing stones A1 and A3.

As you can see from the following list, there are of both printing stones panes which occur twice Thus this is the proof that there are minimum 2 complete sheets of both printing stones with full frame around the cross.
Since the printing stone A1 was printed in the form of two groupes of 40, we can deduct that there are theorectically 2 x 80 pieces of stone A1 with full cross frame.
The stone A3 however was printed in 4 groupes as per 40 types. Consequently the theorectical the total number of Rayon II with full cross frame of this printing stone A3 is 320 pieces. 
In other words the full cross frames of printing stone A1 are theorectically twice as rare as those of printing stone A3!

Let us examine how this looks correctly:

              
Comment:
According to my personal experience there should be today about 8 % of all Rayon stamps preserved. If somebody means only 6 % or more even 10 % we can talk. With every further year the chance dimishes to discover still unknown archives and see more copies on the market.Therefore new discoveries will keep within limits.
Among the the figures named above are pieces included which were published and expertized. But also included are pieces that may not have survived the turmoil of two world wars or fires etc. We ourselves experience the loss of one of such rayons sent by registered letter to the United States in 2011, which got stolen and was destroyed afterwards according to the thief! So the above list of existing copies must be adjusted and reduced by such losses.

Among the covers of stone A1 it is surprising to see that these are more numerous than one would think considering the frequency usage reason A1 : A3
The explanation is simple : all four covers were written by Grandson to Mr. R. Charbonnier in Aubonne! It is of course a coincidence that one found in one single archiv so many world rarities and also that this archiv found its way onto the market! Similiar accumulations are also known about other stamp issues. I would just remind you about the Basle Dove covers of the Ryhiner archive or those to Mr. Riggenbach in Basle or out of Geneva the many covers to the Minister Claparède or the lovely family correspondence of Madame Barrilliet to her son to the boarding school Naville in Vernier or a little later all the Ortspost covers to Miss Zellweger in Bischofszell. Such archives can – if they ever come on to the market at all- lead to distortions statistically and change our assumed established lists.