One thing that may be confusing your attempts to join the polygons, is that the polygons returned from M::G::V->polygons can contain duplicate points. Are you aware of this?

By way of example, the following creates a regular grid of 9x7 equi-spaced points and the uses M::G::V to compute and return the polys. The result is 35 (7x5) "square" polygons. But each of the polys return has 6 rather than 4 points? With 2 points being duplicated in each poly. This doesn't affect the drawing of the polys, but it gets confusing when trying to manipulate the edges.

#! perl -slw
use strict;
use Data::Dump qw[ pp ]; $Data::Dump::MAX_WIDTH = 200;
use Math::Geometry::Voronoi;

my @points = map{
    my $y = $_;
    map [ $_, $y ], map $_ * 100, 1 .. 9;
} map $_ * 100, 1 .. 7;

my $geo = Math::Geometry::Voronoi->new( points => \@points );
$geo->compute;

my @geoPolys = $geo->polygons;
pp \@geoPolys;
[download]

Produces:

C:\test>voronoi
[
##     {**** duplicates ****}              {**** duplicates ****}
  [10, [250, 250], [250, 250], [250, 150], [150, 150], [150, 150], [15
+0, 250]],
  [11, [350, 250], [350, 250], [350, 150], [250, 150], [250, 150], [25
+0, 250]],
  [12, [450, 250], [450, 250], [450, 150], [350, 150], [350, 150], [35
+0, 250]],
  [13, [550, 250], [550, 250], [550, 150], [450, 150], [450, 150], [45
+0, 250]],
  [14, [650, 250], [650, 250], [650, 150], [550, 150], [550, 150], [55
+0, 250]],
  [15, [750, 250], [750, 250], [750, 150], [650, 150], [650, 150], [65
+0, 250]],
  [16, [850, 250], [850, 250], [850, 150], [750, 150], [750, 150], [75
+0, 250]],
  [19, [250, 350], [250, 350], [250, 250], [150, 250], [150, 250], [15
+0, 350]],
  [20, [350, 350], [350, 350], [350, 250], [250, 250], [250, 250], [25
+0, 350]],
  [21, [450, 350], [450, 350], [450, 250], [350, 250], [350, 250], [35
+0, 350]],
  [22, [550, 350], [550, 350], [550, 250], [450, 250], [450, 250], [45
+0, 350]],
  [23, [650, 350], [650, 350], [650, 250], [550, 250], [550, 250], [55
+0, 350]],
  [24, [750, 350], [750, 350], [750, 250], [650, 250], [650, 250], [65
+0, 350]],
  [25, [850, 350], [850, 350], [850, 250], [750, 250], [750, 250], [75
+0, 350]],
  [28, [250, 450], [250, 450], [250, 350], [150, 350], [150, 350], [15
+0, 450]],
  [29, [350, 450], [350, 450], [350, 350], [250, 350], [250, 350], [25
+0, 450]],
  [30, [450, 450], [450, 450], [450, 350], [350, 350], [350, 350], [35
+0, 450]],
  [31, [550, 450], [550, 450], [550, 350], [450, 350], [450, 350], [45
+0, 450]],
  [32, [650, 450], [650, 450], [650, 350], [550, 350], [550, 350], [55
+0, 450]],
  [33, [750, 450], [750, 450], [750, 350], [650, 350], [650, 350], [65
+0, 450]],
  [34, [850, 450], [850, 450], [850, 350], [750, 350], [750, 350], [75
+0, 450]],
  [37, [250, 550], [250, 550], [250, 450], [150, 450], [150, 450], [15
+0, 550]],
  [38, [350, 550], [350, 550], [350, 450], [250, 450], [250, 450], [25
+0, 550]],
  [39, [450, 550], [450, 550], [450, 450], [350, 450], [350, 450], [35
+0, 550]],
  [40, [550, 550], [550, 550], [550, 450], [450, 450], [450, 450], [45
+0, 550]],
  [41, [650, 550], [650, 550], [650, 450], [550, 450], [550, 450], [55
+0, 550]],
  [42, [750, 550], [750, 550], [750, 450], [650, 450], [650, 450], [65
+0, 550]],
  [43, [850, 550], [850, 550], [850, 450], [750, 450], [750, 450], [75
+0, 550]],
  [46, [250, 650], [250, 650], [250, 550], [150, 550], [150, 550], [15
+0, 650]],
  [47, [350, 650], [350, 650], [350, 550], [250, 550], [250, 550], [25
+0, 650]],
  [48, [450, 650], [450, 650], [450, 550], [350, 550], [350, 550], [35
+0, 650]],
  [49, [550, 650], [550, 650], [550, 550], [450, 550], [450, 550], [45
+0, 650]],
  [50, [650, 650], [650, 650], [650, 550], [550, 550], [550, 550], [55
+0, 650]],
  [51, [750, 650], [750, 650], [750, 550], [650, 550], [650, 550], [65
+0, 650]],
  [52, [850, 650], [850, 650], [850, 550], [750, 550], [750, 550], [75
+0, 650]],
]
[download]