Mesh region from mesh edges only

Question

I have a collection of lines ordered by pairs of points, as below, and wish to get a MeshRegion from them, with the mesh edges being the given lines. (That is, the 2-dimensional mesh should be composed of the polygons shown below, with the big space inside taken out.)

Now, I don't want to write explicitly the points and mesh primitive cells because it's too large. Is there a direct way to do it ?

data={{{0.968246, -0.25}, {0.866025, -0.5}}, {{0.968246, -0.25}, {1., 0.}}, {{0.968246, -0.25}, {0.968246, -0.25}}, ... };
Graphics[{Green, Line[data]}]

(complete data set downloadable here or below)

 {{{0.968246, -0.25}, {0.866025, -0.5}}, {{0.968246, -0.25}, {1.,0.}}, 
 {{0.866025, -0.5}, {0.75, -0.661438}}, {{0.75, -0.661438}, \
 {0.661438, -0.75}}, {{0.661438, -0.75}, {0.5, -0.866025}}, {{0.5, \
      -0.866025}, {0.25, -0.968246}}, {{0.25, -0.968246}, {0., -1.}}, 
  {{0., \
 -1.}, {-0.25, -0.968246}}, {{-0.25, -0.968246}, {-0.5, -0.866025}}, \
 {{-0.5, -0.866025}, {-0.661438, -0.75}}, {{-0.661438, -0.75}, {-0.75, \
 -0.661438}}, {{-0.75, -0.661438}, {-0.866025, -0.5}}, {{-0.866025, \
 -0.5}, {-0.968246, -0.25}}, {{-0.968246, -0.25}, {-1., 0.}}, {{-1., 
    0.}, {-0.968246, 0.25}}, {{-0.968246, 0.25}, {-0.866025, 
    0.5}}, {{-0.866025, 0.5}, {-0.75, 0.661438}}, {{-0.75, 
    0.661438}, {-0.661438, 0.75}}, {{-0.661438, 0.75}, {-0.5, 
    0.866025}}, {{-0.5, 0.866025}, {-0.25, 0.968246}}, {{-0.25, 
    0.968246}, {0., 1.}}, {{0., 1.}, {0.25, 0.968246}}, {{0.25, 
    0.968246}, {0.5, 0.866025}}, {{0.5, 0.866025}, {0.661438, 
    0.75}}, {{0.661438, 0.75}, {0.75, 0.661438}}, {{0.75, 
    0.661438}, {0.866025, 0.5}}, {{0.866025, 0.5}, {0.968246, 
    0.25}}, {{0.968246, 0.25}, {1., 
    0.}}, {{-0.75, -0.5}, {-0.5, -0.5}}, {{-0.75, -0.5}, {-0.75, \
      -0.25}}, {{-0.75, -0.5}, {-0.75, -0.661438}}, {{-0.75, -0.5}, \
      {-0.866025, -0.5}}, {{-0.5, -0.5}, {-0.5, -0.75}}, {{-0.5, -0.75},           \
 {-0.25, -0.75}}, {{-0.5, -0.75}, {-0.5, -0.866025}}, {{-0.5, -0.75}, \
 {-0.661438, -0.75}}, {{-0.25, -0.75}, {0., -0.75}}, {{-0.25, -0.75}, \
 {-0.25, -0.968246}}, {{0., -0.75}, {0.25, -0.75}}, {{0., -0.75}, {0., \
 -1.}}, {{0.25, -0.75}, {0.5, -0.75}}, {{0.25, -0.75}, {0.25, \
 -0.968246}}, {{0.5, -0.75}, {0.5, -0.5}}, {{0.5, -0.75}, {0.661438, \
 -0.75}}, {{0.5, -0.75}, {0.5, -0.866025}}, {{0.5, -0.5}, {0.75, \
 -0.5}}, {{0.75, -0.5}, {0.75, -0.25}}, {{0.75, -0.5}, {0.866025, \
 -0.5}}, {{0.75, -0.5}, {0.75, -0.661438}}, {{0.75, -0.25}, {0.75, 
    0.}}, {{0.75, -0.25}, {0.968246, -0.25}}, {{0.75, 0.}, {0.75, 
    0.25}}, {{0.75, 0.}, {1., 0.}}, {{0.75, 0.25}, {0.75, 
    0.5}}, {{0.75, 0.25}, {0.968246, 0.25}}, {{0.75, 0.5}, {0.5, 
    0.5}}, {{0.75, 0.5}, {0.75, 0.661438}}, {{0.75, 0.5}, {0.866025, 
    0.5}}, {{0.5, 0.5}, {0.5, 0.75}}, {{0.5, 0.75}, {0.25, 
    0.75}}, {{0.5, 0.75}, {0.5, 0.866025}}, {{0.5, 0.75}, {0.661438, 
    0.75}}, {{0.25, 0.75}, {0., 0.75}}, {{0.25, 0.75}, {0.25, 
    0.968246}}, {{0., 0.75}, {-0.25, 0.75}}, {{0., 0.75}, {0., 
    1.}}, {{-0.25, 0.75}, {-0.5, 0.75}}, {{-0.25, 0.75}, {-0.25, 
    0.968246}}, {{-0.5, 0.75}, {-0.5, 0.5}}, {{-0.5, 0.75}, {-0.661438,
     0.75}}, {{-0.5, 0.75}, {-0.5, 0.866025}}, {{-0.5, 0.5}, {-0.75, 
    0.5}}, {{-0.75, 0.5}, {-0.75, 0.25}}, {{-0.75, 0.5}, {-0.866025, 
    0.5}}, {{-0.75, 0.5}, {-0.75, 0.661438}}, {{-0.75, 0.25}, {-0.75, 
    0.}}, {{-0.75, 0.25}, {-0.968246, 0.25}}, {{-0.75, 
    0.}, {-0.75, -0.25}}, {{-0.75, 0.}, {-1., 
    0.}}, {{-0.75, -0.25}, {-0.968246, -0.25}}}

Answer 1

• data[[3]], the two endpoints is the same, so it is the degenerate line, Mathematica auto remove it.

Clear[pts];
pts = DeleteDuplicates[Flatten[data, {2, 1}]];
MeshRegion[pts, {Point /@ Range@Length@pts, 
  Table[Line[Flatten[FirstPosition[pts, #] & /@ d]], {d, data}]}]

$Version

"13.1.0 for Microsoft Windows (64-bit) (June 16, 2022)"

• We use Planar graph to find such small polygons.
• We delete the longest two circles.

Clear[pts,edges, g, faces, reg];
pts = DeleteDuplicates[Flatten[data, {2, 1}]];
edges = Table[
   UndirectedEdge @@ Flatten[FirstPosition[pts, #] & /@ d], {d, data}];
g = Graph[edges, VertexCoordinates -> Thread[Range@Length@pts -> pts]];
faces = PlanarFaceList[g];
faces = SortBy[faces, Length][[1 ;; -3]];
reg = MeshRegion[GraphEmbedding[g], 
  Polygon[faces /. First /@ PositionIndex[VertexList[g]]]]
MeshPrimitives[reg, 2]

Answer 2

First, discretize it:

mesh = DiscretizeGraphics[Graphics[Line[data]]]

Find polygon faces:

face = Select[PlanarFaceList[MeshConnectivityGraph[mesh]], 
    Length[#] <= 5 &][[All, All, 2]];

Construct mesh:

MeshRegion[MeshCoordinates[mesh], Polygon[face]]