Rombo

Rombo is a boardless strategy game in which players add pieces to a steadily growing cluster in an effort to cut off enemy areas.

Play: Each turn the current player must add a rombo of their colour to the cluster. The new rombo must exactly meet at least two faces of existing rombos. It is not allowed to form closed holes which would make the cluster hollow.

Aim: A player wins by splitting the visible enemy faces into two or more disjoint sets. If neither player achieves this before the pieces run out then the game is a draw.

For instance, the following figure shows two games won by White, who has split off a subset of visible Black faces in each case. The figure on the left (a) demonstrates that faces must share an edge to be considered adjacent (faces do not connect across corners).

The following example shows a longer game won by Black, who has cut off a single visible White face.

Each rombo is actually a rhombic dodecahedron, which is a convex polyhedron formed by twelve identical rhombic faces with a dihedral angle of 120 degrees, and the dual of the cuboctahedron.

A packing of rombos will fill 3-dimensional space in a honeycomb pattern equivalent to the face-centred cubic lattice found in cannonball stacking. However, each layer of rombos within the packing will orient the layer directly above and directly below, neatly avoiding phase problems that plague sphere-stacking games on the hexagonal grid. See Cubox and Lazo for other ways to solve phase problems in such games.

Note: The winning condition can be made stricter by requiring that players form a loop of their pieces to cut the visible enemy faces into disjoint sets. In this case, the first win example shown above (a) would no longer be a win as White has not completed a loop around the threatened Black area (faces now connect across corners). One more White piece is required at the lower right to complete the win.