alkaline wrote:yes send me some pictures, this is quite some mind-boggling stuff
Aale de Winkel wrote:Yes pictures please, also to the hyperoctagons.
shaving off the hypercubes corners I fully understand, but blowing out faces can be done ad infinitum even to the point where one ends up with an hypersphere.
Aale de Winkel wrote:numbernotatation, if I now understand it:
1: line
2: circle
3: sphere
so:
12: line-circle so cylinder (but how to denote a cone)
13: line-sphere so spherinder (but what about the sphone)
Aale de Winkel wrote:22: circle-circle so duocircle (why this was confused with "duocylinder" 1212(?))
though using this notation 122 would be the first pentaspace object that might be called a duocylinder (which means that 1212 contracts somehow to 122(?), though I do think 1212 is a hexa-space object, which is different from 1122 (the duocubinder(?)))
Aale de Winkel wrote:Is there a way to describe the donut in this manner, which is thus 12 but the 1 is circling the "but" onto the "face" circle.
A notationally confused trionian
Aale de Winkel wrote:It might be a too simple thought, but given the pictures, is a dodecatwister not simply a twisted dodecahedron, this allows simular notation as above, though twisting remains in the same dimension.
Aale de Winkel wrote:http://hometown.aol.com/Polycell/uniform.html
shows excellent picture of what might be call polygoncylinders, lets say P[sub]p[/sub] to stand for the p-agon (ie p-corners) then:
P[sub]p[/sub]1 : the p-agon cylinder (p-agon prism (!?))
this notation generates tip (p = 3) cube (p = 4), pip (p = 5), hip (p = 6) sip (p = 7) oip (op(??) p = 8 ) nip (p = 9) dip (p = 10) the same way as when using spherical based cylinder types
The shown pantagonal antiprism can simular be handled but needs some other "extrudor" lets say '>' then
P[sub]p[/sub]> : the p-agon anti-prism
thus generating tap / dap (the page shows only pap, don't know wheter p=4 would be called cap in which case cube = cip (hip from hexahedron won't do because of p=6))
Aale de Winkel wrote:introducing in this post:
F: filling: fillng the object: circle --> disc, sphere --> ball etc.
-: subtracting: subtracting objects of different size: circle - circle --> docircle(? = ring! ?); ball - ball --> doball
(one needs to add size-parameters to define subtraction more presicely.)
adding could also be defined for the unfilled types, however I consider this only for objects of same type, assuming by default the subtracted to be of say half size of the other, subtracting filled objects from filled objects is therby solidly defined, while adding here is quite redundant. With unfilled object one simply needs to ignore the technically present sign, or define addition also introducing the different objects T+T and T-T (with T=triangle)
Aale de Winkel wrote:Probably this is not the full range. The step from say triangle --> hexagon; square --> octagon, could also be formalized. I currently don't see pentagon and heptagon easily formulated, but the p-agon P[sub]p[/sub] is easily defined, as most likely other basic entities need be defined.
The lettering is adhockly defined and preliminairy at best, Polyhedron Dude please your comments on this monolog. I realize that my "polygon-cylinder" has some friction with your prism-sequence, but far easily to grasp then the schlaefli symbols etc. :wink:
Aale de Winkel wrote:squap and squip I understand, 8P "op" I read on http://hometown.aol.com/Polycell/uniform.html , trip was simply not printed on my paper copy , trap also is logical then , 9P ep (it is simply the first time I read "enne" for 9)
Aale de Winkel wrote:"op" as I understand your mnemonics, you take first letter of the regular name and trow in some letters to make them pronounceable, which thus makes "op" equivalent to "oip", for me though "oip" makes it more stand apart for "oap" (thus defining 'i' the normal prism, and 'a' the antiprism connector, with 'c' the "conicalizer" one could have a sloidly defined oc, but probably need some vocal to pronounce "trc" ).
Aale de Winkel wrote:(what you mean with "bloated circularly" I don't know, probably because I'm no a native english speaker :? )
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