Copyright issues restrict my displaying Professor Karst Hoogsteen’s work on the nucleoside here. However, anyone seriously interested in this proposal could glean much from the papers he published in Acta.Crysta between 1959 and 1963. They are formidable pieces of work that have been ‘long buried’ precisely because they contradicted Crick/Watson’s base pairing solution. In fact his work directly supports the pentagonal pairings I propose - in every instance and diagram he illustrates the pentagonal part of the purine hydrogen-bonding with the pyrimidine.  

He states categorically that, given free will, the molecules refused to pair in the fashion proposed by Crick and Watson. In fact the large and beautifully illustrated diagram on page 913(1963) actually shows a collapsed version of the A/T keto base pair illustrated in my publication. He also states that he did not have as much success with G/C pairings as with A/T and this I believe is quite likely to be a result of the blocks that he placed on the respective 1 and 9 nitrogen positions. I do mention in my catalogue that the geometric proposal would require N9 of guanine to be available to form hydrogen bonds, as indeed was still the case prior to 1953.

Furthermore, patterns and structures formed utilising the pentagon destroy geometric congruence, a necessary means by which energy can and is able to dissipate. For this reason the pentagon is deemed unsociable, thereby ‘focusing' energy rather than ‘dissipating' it. Congruence allows energy to flow seamlessly whilst incongruence focusses energy. (Johannes Kepler - Harmony of the World, Book II, prop IX)

It would be very interesting to repeat Hoogsteens research, especially with respect to Guanine and Cytosine, without blocking any of the potential hydrogen atoms but especially N9. 

As a point of note: I do appreciate that bond lengths and angles will not adhere precisely to that of the mathematical structure.  It is the overall principals of helical generation that I am concerned with and I would therefore expect a relative degree of variation. Perhaps as much as 9.5 to 10.5 bases per helical turn.