check-cubes.pl6

use v6;

my @adjacentVertices =
  0, 1,
  0, 2,
  1, 3,
  2, 3,
  4, 5,
  4, 6,
  5, 7,
  6, 7,
  0, 4,
  1, 5,
  2, 6,
  3, 7;

sub checkCube(@vertices) {
  for @adjacentVertices -> $v1, $v2 {
    my $diff = (@vertices[$v1] - @vertices[$v2]) % 8;
    return False if $diff == 1 || $diff == 7;
  }
  return True;
}

my $c = 0;
for permutations(8) -> @vertices {
  if checkCube(@vertices) {
    ++$c;
    say "  {@vertices[2]}---{@vertices[3]}";
    say " /|  /|";
    say "{@vertices[0]}-+-{@vertices[1]}";
    say "| | | |";
    say "| {@vertices[6]}-+-{@vertices[7]}";
    say "|/  |/";
    say "{@vertices[4]}---{@vertices[5]}";
    say "";
    say "";
  }
}
say "Total: $c (p = {$c / 40320})";