Polygrams
Given, say, a hexagon, we can construct a new one by the
following procedure.
- find the point where the line determined by
points 1 and 3 intersects the line determined by
points 2 and 4.
- find the point where the line determined by
points 2 and 4 intersects the line determined by
points 3 and 5.
- etc.
This procedure gives 6 new points. The figure shows
two of these points.
The solid cyan point is where the line
determined by 6 and 2 intersects the
line determined by 1 and 3. In the
ordering of the points, 6 comes before
1, and plays the role of 0 in the construction.
Of course, there's nothing special about hexagons.
We could make the same construction, in the
same way, for any polygon.
On an octagon, we would call this construction
the octagram.
On a 10-gon, we would call this construction
the 10-gram And so on.