Creating a UV Map from a shrinkwrapped sphere I'm not quite sure how to explain this, but I try as good as I can:
I want to create a UV Map for a room with 8 walls that has a sphere shrinkwrapped onto it, so I can project equirectengular video material on it.
Has anyone experience with this?
So far I build the room:

and I shrinkwrapped a sphere onto it:

but the borderlines are weirdly pressed together so it's not just a clean edge and the corners are also filled incorrectly, is it normal in my case?
Do I have to merge along the vertices and the edges at the borderlines manualy, so that I can make a seam there for the UV?
Is there a better solution to shrinkwrap a sphere onto such an object to get a clean spherical UV?
Thanks for any hints
Spherical projection

The above is the equirectangular projection of the Tissot Index Plate Carrie projection image found here Justin Kunimune / CC BY-SA (https://creativecommons.org/licenses/by-sa/4.0)  onto a squashed 8 sided ngon filled cylinder.

The node set up explained in this answer https://blender.stackexchange.com/a/159492/15543
A Hammer Projection
and again using a Hammer Projection node setup as explained here of
Tissot index hammer projection image from wiki by Justin Kunimune CC BY-SA 4.0