by wendy » Wed Nov 28, 2007 7:39 am
The manner of describing polytopes is to use a concept of a number of patches, eg polyhedron actually means 'many seats'. The same root is seen in cat.hedr.al = over.seat (the place where the bishop (episciple) sits. Episcile = epi (all) + scope (see).
In any case, there is some confusion over the established terminology in mathematics, because /poly.gon/ actually is 'many knee', with gon and knee being the same word. Various reformers have advocated some kind of consistancy in the termonology.
Since the PG is intended to go to many dimensions, it implements the notion of 'fabric of space', (words in -ix), and 'patches of such fabric' (in -on.). So hedrIX is the fabric of 2-space, and hedr-ON is a specific patch.
The prefix applied to /hedron/ is then something one does with said patches. The usual pattern is to apply a numerical prefix, with the intent that such closes the figure. So a tetra.hedron is 4 2-patches that make a closed figure.
One can use other descriptive words to say an effect, rather than a count. 'apeiro' means 'without a perimeter (in space)' a = without (cf a.tom = without division), peri or peiro = boundary (cf perimeter). An a.peiro.hedron is patches laid in a plane without a perimeter: a 2d tiling.
One then distinguishes between /poly/ = many + closure, against just /multi/ = many. A miltihedron is not nessecarily closed, a partial polyhedron for example.
Likewise, 'hedrix' is used for 2d cloth, or manifolds. With suitable prefixes, it takes on assorted shapes too. A plato.hedr.ix is a flat+2d+coth (ie a plane). A glomo.hedrix = round+2d+cloth = sphere. A glomohedron is the corresponding sphere with interior.
By replacing /hedr/ with 3d /chor/, 4d /ter/, 5d /pet/, 6d /ect/, 7d /zett/ and 8d /yott/, one has ready-made names for figures bounded by these fabrics or patches. We for example, live in a horo.chor.ix, = horizon-centred + 3d + fabric. Hyperbolic 4-space would be a bollo.ter.ix. And so forth.
The actual metric prefix for E18 is 'Exa' greek /hexa/. However, the corresponding cloth would be *exix, which mutates under euphonics to 'ectix'. Since /ex/ is already an active prefix meaning "out of, former", it was decided to backform 'ect' throughout the whole of six dimensions.