John G
The Living Force
Yeah it could be double tetrahedron equals octagon from our 3D point of view as in our normal 4-dim spacetime plus another 4-dim Kaluza-Klein-like space and for the 4D hexagon given that Ark clarified the 4D is space-like, you could have Ark's 6-dim conformal geometry which does create complex domains. Given the " Tetrahedron in 3D is what in 4D?", the space-like part might be 5-dim which would fit with for n=4:Ark,
I was thinking something like this gives something that can be mapped into a hexagon but using the outer 6 points and it is an octogonal complexigram of sorts.
Klein geometry - Wikipedia
en.wikipedia.org
Conformal geometry on the sphere... Lorentz group of an ( n + 2 ) dimensional space O ( n + 1 , 1 )
You would have a 4-dim conformal metric with an O ( 5, 1 ) conformal structure group.
Simplex - Wikipedia
en.wikipedia.org
- a 0-simplex is a point,
- a 1-simplex is a line segment,
- a 2-simplex is a triangle,
- a 3-simplex is a tetrahedron,
- a 4-simplex is a 5-cell.