Prashantkrishnan wrote:Is the bicircular tegum an irregular duocylinder? [...]
quickfur wrote:Prashantkrishnan wrote:Is the bicircular tegum an irregular duocylinder? [...]
The bicircular tegum can be thought of as the dual of a duocylinder, i.e., replace the two bounding torus-shaped surface patches of the duocylinder with two circles, which lie in orthogonal planes, and take the convex hull of that. It's the pyramid product of two circles, whereas the duocylinder is the cartesian product (prism product) of two circles.
quickfur wrote: the bicircular tegum (Cartesian product of a circle with smaller circle)
Prashantkrishnan wrote:quickfur wrote:Prashantkrishnan wrote:Is the bicircular tegum an irregular duocylinder? [...]
The bicircular tegum can be thought of as the dual of a duocylinder, i.e., replace the two bounding torus-shaped surface patches of the duocylinder with two circles, which lie in orthogonal planes, and take the convex hull of that. It's the pyramid product of two circles, whereas the duocylinder is the cartesian product (prism product) of two circles.
I do not understand many of these terms. For example, I don't know what a convex hull or a pyramid product is. And also, what does a dual mean for shapes other than polytopes?quickfur wrote: the bicircular tegum (Cartesian product of a circle with smaller circle)
If it is the Cartesian product, then won't it just be a duocylinder with one radius smaller than the other? Or is it the pyramid product only and not the Cartesian product?
ICN5D wrote:Now I understand the bi-circular tegum. That one was a fog until now. So, it's kinda like a 4D version of a crind. The 'shrinkwrapping' description is what worked, visually. I wonder what the implicit definition would be? Surely, there's a way to procedurally derive it, much like the other new shapes I did recently. Anybody look into functions for tegums, preferably non-parametric? Parametric is okay, but I don't understand how it works as much as implicit.
Return to Higher Spatial Dimensions
Users browsing this forum: No registered users and 57 guests