How to obtain the following topology?

Question

My follow up question: How can I use a pivot circle instead of a pivot point

Question

At this moment, I have this:

What is the most efficient way to achieve a quad as cut section, where

• all the faces as well as the unselected vertices are duplicated and overlapping
• but share the same vertices (selected).

The cut section would look like this:

Answer 1

Unless I've severely misunderstood what you're trying to achieve, I still think a torus with Minor Segments set to 4 is the easiest and quickest way.

ShiftA followed by M followed by T or Add -> Mesh -> Torus to add the torus.

After adding it and changing Minor Segments to 4, just scale along Z, S followed by Z, then type in the scale or drag the mouse, and finish with Enter or LMB.

Answer 2

Alternative 1

I tried the following:

• E to extrude the selected vertices, S and Y and 0 to scale relative to the y-axis
• Then remove the doubles

Alternative 2

• First add a plane and rotate it 90 degrees around y-axis and rotate it 45 degrees around x-axis
• scale along z-axis

It could be a solution to my own question and hence I posted this as an answer to my own question, but perhaps you have a more efficient solution