From: Robert Lang <[email protected]> indited: >In 1509, Luca Pacioli and Leonardo da Vinci put together a book, "La Divina >Proportione," in which they introduced the concept of erecting a pyramid on >each face of a >polyhedron (which is what is effectively happening in a Sonobe >solid) and they called the operation "Elevation." So Sonobe solids would be >(according to that terminology) >"elevated polyhedra," and that's the term >I've used when describing modulars with that form. Here's a Bridges paper that >gives details:
There do seem to be lots of names for similar aspects of this process. So ... as a non-mathematician I venture intrepidly into mathematical territory ... happy to have my misconceptions and mistakes pointed out. At least the following possibilities seem to exist: Elevation Accretion Cumulation Akisation (from the Conway operator kis) Kleetope Pyramidisation or pyramid-augmentation There are also the triakis polyhedra which can be derived through this process, though they appear to be special instances, as are those stellated polyhedra which can also be derived in this way. George Hart suggests that elevation is also a special instance, the addition of pyramids with equilateral faces, but I do not know if this is an authoritative view. I am not clear what the process of forming a Kleetope is and whether it is a specific process or a general one. Of the remaining general terms I tend strongly towards cumulation because it means, or can mean, 'forming into a pile' which seems to make sense in terms of the process. Negative cumulation? Surely not? Excavation, perhaps? And then, of course, I have myself been using pimpled and dimpled for years! Dave
