Drawing symmetrical objects

Recent request on tech support was how to close the elements of an imported DXF:

The file in question came in as polylines:

while one would prefer it to be composed of curves which will be more elegant.

Select the design and put everything on a locked layer:

Then draw geometry as appropriate to define the arcs and other circle segments:

Go into Node Edit mode and add nodes and then cut the vectors as appropriate to allow re-using those portions of the circle which are coincident w/ the design:

Then draw in lines/curves to connect everything:

Join the curves/arcs/polylines:

and edit until one arrives at:

Draw a centered circle larger than all the geometry:

Draw a line from the center to the beginning point:

Count the number of elements — 12, rotate by that number divided into 360 == 30:

Edit as necessary to make things line up:

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Then duplicate the geometry 11 times:

Align the duplicates w/ the original:

shift-click to deselect one, and shift-click to add the circle to the selection:

rotate by 30 degrees:

shift-click to deselect one and repeat until one arrives at:

delete the line and circle and select everything:

and Join to arrive at:

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