Creating a list polygon's vertices from two lists of points

Question

I would like to construct a list of polygons by using two different lists of points:

list1={{0, 0.}, {0, 1.18961}, {0, 2.37923}, {0, 3.56884}, {0, 4.75846}, {0, 5.94807}, {0, 7.13769}}

list2 = {{2.70289, 0.512313}, {2.47741, 1.70193}, {2.25193, 2.89154}, {2.02645, 4.08116}, {1.80096, 5.27077}, {1.57548,6.46039}, {1.35, 7.65}}

The sequence/function that I tried to use to build the vertices of the polygons (5 points) is:

fpoly[a_Integer, x_List, y_List] = {x[[a]], y[[a]], y[[a + 1]], x[[a + 1]], x[[a]]}

That option does not work. I think if a type of evaluation control is used the fpoly might be an option, but I do not know how to implement it.

To build all the polygons from fpoly my plan was to use something like:

Table[fpoly[i,list1,list2],{i,1,6}]

Any suggestions, please?

Answer 1

polygoncoords = (Join @@@ 
   Partition[Transpose[{list1, list2}], 2, 1])[[All, {1, 2, 4, 3, 1}]];

polygons = Polygon /@ polygons;

Graph the third polygon (polygons[[3]]);

Graphics[{Blue, Line@list1, Red, Line@list2, 
  EdgeForm[rc = RandomColor[]], rc, Opacity[.5], polygons[[3]]}]

Graphs polygons 1, 3 and 6 (polygons[[{1, 3, 6}]]):

Graphics[{Blue, Line @ list1, Red, Line @ list2,
 {EdgeForm[rc = RandomColor[]], rc, Opacity[.5], #} & /@ polygons[[{1, 3, 6}]]}]

Graph all 6 polygons:

Graphics[{Blue, Line @ list1, Red, Line @ list2,
  {EdgeForm[rc = RandomColor[]], rc, Opacity[.5], #} & /@ polygons}]

Answer 2

We can select two points from the two list alternatively and use ConvexHullMesh to construct the convex polygon.

BTW,Here we have Reverse the order of the second listlist2to keep the orientation of polygon,so we can also replace ConvexHullMesh by Polygonto make the same convex polygons.

list1 = {{0, 0.}, {0, 1.18961}, {0, 2.37923}, {0, 3.56884}, {0, 
    4.75846}, {0, 5.94807}, {0, 7.13769}};

list2 = {{2.70289, 0.512313}, {2.47741, 1.70193}, {2.25193, 
    2.89154}, {2.02645, 4.08116}, {1.80096, 5.27077}, {1.57548, 
    6.46039}, {1.35, 7.65}};
polygons = 
  ConvexHullMesh /@ 
   Join @@@ Tuples[{Subsets[list1, {2}], Subsets[Reverse@list2, {2}]}];
i = RandomInteger[{1, Binomial[7, 2]^2}]
Graphics[{{EdgeForm[Green], FaceForm[Directive[Opacity[.5], Yellow]], 
   polygons[[i]]}, {Red, Point[list1], Arrowheads[.1], 
   Arrow[list1]}, {Blue, Point[list2], Arrowheads[.1], Arrow[list2]}}]