Polygonal Tori

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration shows a torus with a polygonal cross section.
[more]
Contributed by: Erik Mahieu (July 2015)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The parametric equation of a circular torus with a polygonal cross section is obtained as follows.
The parametric of the ring circle with radius is:
.
The polar equation of a regular -gon with circumradius
is:
.
Using the Mathematica function FrenetSerretSystem, we define the normal and binormal vectors and
:
.
This gives the parametric equation of the elliptical torus:
,
with vertices and
the circumradius of the cross-sectional polygon.
Expanded, with , this becomes:
,
,
.
Permanent Citation