#!/usr/bin/perl
use strict;
my @seg = (
    [ 1, 1, 2, 1 ],
    [ 5, 5, 1, 5 ],
    [ 2, 3, 5, 3 ],
    [ 5, 3, 5, 5 ],
    [ 2, 1, 2, 3 ],
    [ 1, 5, 1, 1 ]);

my %starts=map{"@$_[0,1]",$_} @seg;
my @sorted_segs = my $cur = $seg[0];
while (1) {
  my $next = $starts{"@$cur[2,3]"};
  die "your polygon is broken\n" if !$next;
  $next==$seg[0] ? last : push @sorted_segs,$next;
  $cur = $next;
}

print "@$_\n" for @sorted_segs;