@DavidKButler
#Midpoint-stretching polygon

David:"A polygon is cyclic when you can draw one circle through all its vertices. I know not all pentagons are cyclic. I wonder: How do you tell if a pentagon is cyclic or not?"
Ray: "Probably normals to the midpoints of sides have to intersect at one point."
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Here is an elementary construction going from a Cyclic polygon to midpoints.

Part 2; construction of a unique polygon from midpoints is undetermined (to me); see below.

Part 1: Redefine the problem (Cynlic Polygon) to a collection of points with an equidistant center.
2) Draw the radii (i.e. line to that center). And connect the points to form the edges.
3) Now we have a sequence of isosceles triangles. Things we know a lot about; including those altitudes from the center that intercept our ledges are right angle and equidistant from the associated vertices.
4) We have shown that a Cyclic Polygons edges have unique isosceles triangles associated with them that can be split in two; i.e. midpoints. So the midpoints have to meet in the center.

Part 2: Take a collection of "midpoints" and construct a polygon. Is it unique?

I think so. The relevant mathematical term seems to be
"Midpoint-stretching polygon".
but is usually referring to interior/recursive generation; not exterior generation.
I will think about it and see if I can prove it. Dissecting the midpoint polygon and a proposed exterior constructed polygon seems constrained enough to determine uniqueness; pro or con.

Halbzeit im Romanprojekt! Also beim #Schreiben der Rohfassung, um genau zu sein. Da fehlen natürlich noch ein paar Zwischen-Szenen und dann das ganze #Überarbeiten, #Lektorat und alles. Aber trotzdem ein kleiner Meilenstein. =) Aktuell liefe es auf etwa 320 Seiten raus, ich möchte aber diesmal eher so 420-450 schaffen. Na, mal schauen, was am Ende tatsächlich noch fehlt. #Projekt1930 #Heldenreise #Midpoint #Autorenleben #writerslife #indieauthor