I think this may create the points you need, in a simpler manner (I used a spreadsheet, because it is easier, but this could be done inside QGIS, too:
a) You want "n" points, in your case, 23. Calculate the value of 2*pi/n. This is the angle between each of your points [ "angle" ]
b) Create a column ["ID"] with the numbers 1 to n ; n=23 in your case
c) in the next two columns, save the results of this expression:
sin( angle * (ID-1)); The first ID is really at 0 degrees
cos( angle * (ID-1))
These are the x-y coordinates of all your points
d) Create 2 more columns. These will be the other endpoints for line segments. Insert all the values from the first two columns, but shift down one row: Row 2 for this pair of columns contains the values for Row 1 in the first pair of columns.
e) for row 1, of this second pair, place the value of row n (23) of the first column
You now have 5 columns:
First column is the point ID
Columns 2-3 and Columns 4-5 represent the line segments
So, now you have: points, line segments, or a polygon, depending on what you do with the data.
I crafted a spreadsheet to do this in about 2 minutes. If I were using it, I would export the excel spreadsheet to CSV or somesuch, and import as needed, that is, into points, lines or a polygon.
If I figure out how to import a spreadsheet, here, or post an image at least of it, I will.