Hayate wrote:I changed your "tesseractinder" to a "tesserinder" (the proper name) and your "duocubinder" to a "duocylindrical prism" (to avoid confusion, since a duocubinder would usually refer to a 6-dimensional shape). Please don't take offense.
I would like to know more about your systematic way of finding the names and notations of all the strange, exotic shapes.
Then I noticed there was strange shape called the cylcyltigerinderindric torus and had number 30117. This is why I really would appreciate it if I could learn more. It seems as if there may be a computer program that is computing all of these crazy shapes.
((II)(II)I)I'(II)I
This complicated-looking shape can be dissected for better understanding. Since there is a torus product ((n)I) , we'll start with that one : inside the torus, we find a duocylinder (II)(II) , making a duocylinder torus ((II)(II)I) . This torus is now mult by a triangle I' .
triangle product
I also wanted to ask you if the names are computer generated, too.
And, I especially like the cleverness of the torus notation ((II)I) it makes complete and total sense to me : a circle (II) extruded along the path of a circle(nI).
spin
No, (II) means to extrude a line along the path of a circle, which can be represented as (nI) .To see this interpretation in action, consider the torus, ((II)I) . The format of the operations are in (nI), which means that it has the shape of a circle. The tricky part is to apply the concept of a circle for "n" in the generalized circle notation. This makes the torus, ((II)I) , which means to extrude a circle along the path of a cirlce: "n" is the embeded surface object of the circle (nI) . The number of extrusions that follow the surface object denote the dimensionality of the path to follow. So ((II)II) is the toracubinder, which is a circle (II) that has been extruded along the path of a sphere, denoted as (nII) .Then you are saying (II) means to extrude a line along the path of a line?
Yeah, you'll have to excuse my earlier nomenclature on this subject. My personal interpretation of an extrusion followed by a taper is to condense the two operations into a more elegant form of saying a triangle operation. Still keeping in mind that the order of operations is not commutative, the same can be applied to the double extrusion being called a square operation.There is no such thing as a triangle product!
quickfur wrote:The product of a triangle and a cylinder is just a triangular cylindrical prism (or 3-prismic cylinder)
wendy wrote:quickfur wrote:The product of a triangle and a cylinder is just a triangular cylindrical prism (or 3-prismic cylinder)
There is no single product: there are several different products, not just one. A triangle #* cylinder gives the triangle-line-circle prism.
[...]Speration corresponds to taking a frame (eg vertex + edge), and replacing each point by a sphere of fixed size. This would, for instance convert an edge into a pipe, or a hedron (eg triangle) into a slab with rounded edges. It is not a product but an effect (like truncation, rectification), applied to a framework.
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