wendy wrote:There are a number of base products, based on the w,x,y,z axies, as follows.
[] = prism ie max() maximum
() = spheric ie rss() root-sum-square
<> = tegum ie sum() sum of
Rob wrote:Right. *randomly decides to write out possibilities*
1D
[x] = line
2D
[xy] = square
(xy) = circle
There is no <s>spoon</s> triangle...
3D
[xyz] = cube
[(xy)z] = cylinder
(xyz) = sphere
([xy]z) = ?
<xyz> = octahedron
<(xy)z> = circular tegum
There is no <s>spoon</s> torus...
*shot for the matrix references*
4D
[xyzw] = tesseract
[(xyz)w] = spherinder
[(xy)zw] = cubinder
[(xy)(zw)] = duocylinder
[<xyz>w] = octahedral prism
[<(xy)z>w] = circular tegal prism
[([xy]z)w] = ? prism
(xyzw) = glome
([xyz]w) = ?
([(xy)z]w) = ?
(<xyz>w) = ?
(<(xy)z>w) = ?
Can someone fill in the question marks?
I don't like this notation. There are no torii, and there are no triangular shapes. So bleh!
bo198214 wrote:Hm, now the confusion gets started.
The usage of [] and <> of wendy is quite different to the usage of () in RNS, at least what I can see from the examples.
So wendy can you point out *exactly* how your products are defined?!
I.e. how do we come from such an expression to the implicit equation?
For example:
((xy)z) would be a torus
([xy]z), [(xy)z], <(xy),z> .... would be in my interpretation also be a torus but with one rectangular circle. For wendy the last one is a bipyramid.
[<xy><zw>] tesseract, literally, "rhombus-rhombus duoprism" yeah, I should have noticed that!
[(xy)<zw>] circle-square prism also should have noticed the one, it's what I call the narrow cubinder
[(xy)(zw)] duocylinder [correct]
<[xy][zw]> 16choron the <xyzw> is the hexadecachoron, so this would be the wide hexadecachoron like <[xy]z> is the wide octahedron
<[xy](zw)> square-circle tegum what kind of shape is this? any info on it?
<(xy)(zw)> bi-circular tegum see above
([xy][zw]) duocrind [the name is not known by me] duocrind = crind of a two squares, as the ordinary crind is the crind of a square and a line: ([xy]z)
([xy]<zw>) bi-square rotation Hmm... narrow duocrind
(<xy><zw>) ditto doubly-narrow duocrind
wendy wrote:The thing is that a square [xy] is also a rhomb <xy>
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