Contrary to appearances, Dominions is a Go variant, and contrary to custom, its liberties are situated on the pieces rather than on the board. There are 63 white and 63 black pieces in the game and the white ones look like this:
There's one piece with 6 liberties.
There are six pieces with 5 liberties.
There are fifteen pieces with 4 liberties.
There are twenty pieces with 3 liberties.
There are fifteen pieces with 2 liberties.
There are six pieces with 1 liberty. Pieces are distinguished by a simple binary code, the basis of which is the value of each of the six 'ones'. To determine a piece's number, simply add the powers of two concerned. Since the mindsports applet features 'click and place', this only matters for a game record.
Of course there's also a piece with 0 liberties but it doesn't feature in the game, except as move and score indicator in the applet. It is part of the set however, and the complete 64-set is known as "The China Labyrinth".
Pieces must hook up to the evolving groupsfight. A placement must contact an opponent's piece, and match in terms of blank edges and liberties. Note that the outward edges of border-cells are considered neutral blanks. Thus the maximum match for a cell on the side is an 'unbroken four', for a corner an 'unbroken three'. A piece or group that loses its last liberty is flipped to display the same beam pattern in the opposite color. Dominions thus features othelloanian capture. Suicide moves are legal and in fact essential. Note that pieces cannot rotate: each pattern of liberties is present exactly once. Here's an example position after black 11. The rightmost black piece was a suicide move by white, to deprive black of a liberty and potential extension.
The screenshot is from this example game: http://mindsports.nl/index.php/the-pit/dominions-526.
Though strategy is largely unknown, creating groups that live unconditionally is a sure part of it. Tactics to achieve this are varied and subtle. If a group has a liberty at a cell for which the opponent has no longer a matching piece, this cell is called an "eye". A group with an eye lives unconditionally. An eye of one player's group(s) is not necessarily at the same time an eye of the opponent's group(s) that may have liberties at it: a player may still have one or more matching pieces for a cell, while his opponent doesn't.
Dominions was invented by Christian Freeling in 1984.
Dominions at mindsports: http://mindsports.nl/index.php/the-pit/dominions-526
Turnbased play: http://mindsports.nl/index.php/players-section
The China Labyrinth: http://mindsports.nl/index.php/puzzles/tilings/china-labyrinth/