Thanks for answering Manolo. I'm with you, trying to learn, which is why I was going through the references at hand to see if I could answer your question.
Aylward ("The Smallsword in England", 1945, p.38) notes in a paragraph on 'triple edge blades'.....
"...it is customary to refer to the typical blades of the 18th century as 'triangular', but the term is not quite as accurate as might be wished. In section, the broader side of these blades shows a slightly curved base line from the center of which rises a median spine joined to the extremities of the base line by arcs; in consequence we have a blade which is, in fact, a triple edged one, and the design has come so near to perfection as far as a purely thrusting weapon is concerned that even army bayonets were made in this manner up to a comparitively recent period."
On the next page he notes that these triple edged blades were called 'hollow' blades by those who made them.
On p.36, Aylward notes that an earlier blade, though not intended for smallswords may be the initial development for the 'hollow' blade, forged with a central spine on either side, the four flutes then producing a section resembling a cross with hollowed arms and four edges.
It seems the 'hollow' term may have been misapplied as well as misunderstood with the 17th century sword factories at Hounslow, later Shotley Bridge with the mysterious "Hollow Sword Blade Company" venture , which seems to have been more 'business' than actual production. Later the Shotley Bridge factory claimed to specialize in these 'hollow blades', but no smallswords can definitely be attributed to them as far as is known (p.33).
What I think often adds to confusion is that military blades of latter 18th century onward typically used the hollow ground style where the faces of the blade were ground to form fullers to lighten and strengthen blade.
It would seem the 'hollow' term far exceeded the smallsword blades, and became entirely misperceived in the early days, I believe some perceptions even included the idea that blades were actually hollow with notions of them being filled with mercury and other strange notions.
The actual three equally positioned edges which in cross looks like a three point star is compared to the trialamellum by Burton (p.135), but is of course not comparable to this section.
Im not sure what geometric term would be applicable to these blades of this type section, but wanted to note what they seem to have been called at the time, at least colloquially and probably connected in some degree to these other cases.
I must admit I'm trying to understand these extracts from Aylward as well, so please forgive the drawn out text (for me what else is new
. Perhaps they might give us better perspective at least, but the fact remains the term 'hollow' may not have been used at all for these military version blades.
I think mostly I was working toward understanding the earlier smallsword blades, and possible associations to this one.
All the best,
Jim