Prefixes for Naming Polyhedra
Date: 12/07/2000 at 20:53:46 From: David Subject: Polygons I am having trouble understanding this paragraph that Prof. Conway wrote. Could you please explain it to me? Thank you, David Prof. Conway writes: Antreas Hatzipolakis and I worked out a complete system up to the millions from which this is taken, and which has also been "vetted" by several other scholars. The most important of the reasons which make me prefer the "kai" forms is that they permit these prefixes to be unambiguously parsed even when concatenated, as they are in Kepler's names for certain polyhedra; for example, the icosidodecahedron or (20,12)-hedron, so called because it has 20 faces of one type and 12 of another. Kepler said "this particular triacontakaidihedron I call the icosidodecahedron", a remark showing that he also preferred the kai forms. John Conway See Naming Polygons and Polyhedra from the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.polygon.names.html
Date: 12/07/2000 at 23:16:47 From: Doctor Peterson Subject: Re: Polygons Hi, David. Prof. Conway, like me, is interested not only in math but also in etymology, the study of the origin of words, and is concerned that we form our words consistently, rather than, for instance, accidentally combining Latin and Greek roots in the same word. In this case, he is telling us that he tried to make a consistent system of numeric prefixes with the help of a Greek math historian. He had to make some choices that have not been agreed upon in the past, when it came to putting together prefixes for bigger numbers like 23, where there is no standard prefix. He chose to use the Greek word "kai," meaning "and," rather than, for example, just sticking the two prefixes together (concatenating them). In his example, he points out that his system agrees with the astronomer Kepler, who used these two names for the same thing: icosi dodeca hedron 20 12 faces = 20 faces of one kind, 12 of another triaconta kai di hedron 30 and 2 faces = 32 faces in all By using the "kai" to combine digits of a number (such as 32), his system distinguishes between these two forms; otherwise you might use "triacontadihedron," which could be taken as "30 of one kind and 2 of another." You use "kai" when you mean one number, and leave it out when you mean two. I might have preferred to do it the other way around, but the icosidodecahedron has a long history, and we don't want to change established names. Does that help? Write back if I've left anything out. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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