ICN5D wrote:|>|> : wouldn't that be the duotrianglinder? One of the powertopes as a triangle squared?
|>|00 : lathing a cyltrianglinder into 5D. This creates a cone-like shape out of the spin of the triangular nature of |>|0. Much like lathing a triangle creates the cone, |>|0 is like a flat triangle of cylinders according to 5D. Deriving cylinder-lathe as duocylinder, adding the duo- to cyltrianglinder making duocyltrianglinder.
||>>0 : dicylindrone, lathe of square dipyramid is equal to dipyramid of cylinder [ ||>>0 ] == [ ||0>> ] == [ |0|>> ]. In a strictly worded sense, it has the pattern of "lathe of (square dipyramid)" == "(lathe of square) dipyramid"
|||00 : lathe of cubinder is equal to extrude of duocylinder [ ||00| ], deriving cylinder prism as cubinder, using cub- in place of cyl- for duocubinder, duocyl-prism. I associate |00||0 or ||0|0| as cubspherinder, extrude of cylspherinder |00|0
|>|>> : duotrianglindric pyramid? Going by |>|> as duotrianglinder?
||000 : lathe of duocylinder, If |000| is glominder, pairing the extrude at beginning makes a square as starting shape for duocylinder. It could be the glominder, not sure how to spin the darn thing around that has two curved surfaces into 5D. It can also be written |0|00. But, I know that |00| is not equal to ||00, so it seems that ||000 not equal to |000|.
|00|| : sphere diprism? If |0| is cylinder, |0|| is cubinder, wouldn't |00|0| or |00||0 be cubspherinder of 6D?
|>|0| : also |>||0, cyltrianglinder prism, how do you derive the name cyltriandyinder? Deriving the extrude of cylinder as cubinder, using cub- in place of cyl- for cubtrianglinder
|0>>0 : Disphone, lathe of dicone equal to dipyramid of sphere. Similar to lathe of cone [ |0>0 ] = [ |00> ], [ |0>>0 ] == [ |00>> ] == [ |>0>0 ] == [ |>>00 ], also double lathe of tetrahedron, I'm pretty sure at this point
I'm curious about these, they seem to be 6D if I understand the names correctly. It's the -dyinder suffix, looks like the extrude of something? If |>|0 is cyltrianglinder and you interpret |>|0| as cyltriandyinder, then -linder becomes -dyinder for diprisms?
Here is a picture of the duotrianglinder in fact: https://en.wikipedia.org/wiki/File:3-3_duoprism.png
|>|00 : If that final lathe creates one (and only one) duocylinder and creates a cone-like shape, it could be the cylconinder, which is an object we already have as |0>|0. So the final lathe turns each of the 3 cylinders into duocylinders? I do not see how that would work, as remember the squares in the triangular prism have two different types of edges - edges on one triangular face, and edges connecting opposite triangular faces. Those between opposite triangular faces can easily turn into circles, and thus the squares between them into cylinders, however those on the same triangular face cannot turn into circles, because then the triangle in the middle would turn into a cone in 3 directions at once, which makes no sense.
Okay, then ||000 is the cylspherinder, same as |00|0. Again, was this intentionally listed twice?
cyltrianglinder prism could be thought of as "cyltrianglinder-inder", the "inder" is repeated, so di-"inder", but diinder doesn't read properly, hence i changes to y. "gl" also disappears to make it readable.:
ICN5D wrote:cylconinder
ICN5D wrote:I still haven't grasped how to lathe a duocylinder yet.
A cylconinder is the Cartesian product of a circle and a cone.
One of its tera is a duocylinder and the other is some curved 4-surface. It also includes one circular face. However, its other elements are currently unknown.
If you suppose that the 'O' operator works on the previous constucted axis, then |O|O gives a duocylinder (where the grain runs perpendicular to the circles), and ||OO gives a spherical cylinder (as the circles are spun into spheres).
I haven't yet been able to figure out all the elements of a cylconinder (note the question marks on the wiki page), which doesn't help.
ICN5D wrote:@ wendy, what's this bi-circular tegum you mentioned? You mentioned the dual pyramids as tegums, as in the octahedron being the dual pyramid of the square pyramid. Is the bi-circular tegum like a duocylinder version of this? Or is it more like two circles intersecting at a right angle with the outside envelope smoothing the surface together? I think that's what you mean by skin.
-Philip
Users browsing this forum: No registered users and 1 guest