#!/usr/bin/perl

use strict;
use warnings;

# Input, lines of the figure.

my @l = (
    [qw [A B]],
    [qw [A C F I]],
    [qw [A D G J]],
    [qw [A E]],
    [qw [B C D E]],
    [qw [B F H J]],
    [qw [B I]],
    [qw [E G H I]],
    [qw [E J]],
    [qw [I J]],
);

my %line = ();
my %flat = ();
for my $l (@l) {
  for my $p (@$l) {
    for my $q (@$l) {
      $line{$p,$q}=1;
      for my $r (@$l) {$flat{$p,$q,$r}=1}
    }
  }
}

my @p = 'A'..'J';
for my $p (@p) {
  for my $q (@p) {
    if ($q gt $p and $line{$p,$q}) {
      print "[$p,$q,$_]\n"
      for grep {$_ gt $q and
                $line{$p,$_} and
                $line{$q,$_} and
                not $flat{$p,$q,$_}} @p;
    }
  }
}
[download]

None of that double-$, three-level-deep hashref stuff.

@/=map{[/./g]}qw/.h_nJ Xapou cets krht ele_ r_ra/;
map{y/X_/\n /;print}map{pop@$_}@/for@/
[download]