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An octahedron is composed of eight triangles, four of which meet at each vertex. A regular octahedron can be considered two square pyramids connected base to base as illustrated in FIG-(A). A square pyramid is a pyramid with a square base and four triangles that meet at an apex.
There are 6 vertex cubes in OCTATRIX as illustrated in FIG-(B). Two of them are defined as a ‘Red Pinnacle’ and ‘Blue Pinnacle’. These are where the King is located at the beginning of the game. When the pinnacle vertex surface is attacked by the opponent’s Pawn, the whole army loses and the game is over. FIG-(C) and (D) illustrate the King being attacked by the opponent’s Bishop and Rook. The vertex cubes in OCTATRIX are very vulnerable locations which are easily attacked by the Bishops and Rooks. As a result, the King has to escape to one of the triangular quadrants when it is under attack as illustrated in FIG-(E).
When the vertex cubes are clear ('clear' means free from the opponent's attack), these vertex cubes can be reached by the Bishops and the Rooks within two moves most of the time. FIG-(F) illustrates the Bishop’s move to the vertex cube. As illustrated below, the Bishops can move into one of the vertex cubes within two moves and threaten the King with check positions. FIG-(G) illustrates the Rook’s move to the vertex cube. As illustrated below, the Rooks can move into one of the vertex cubes within two moves and threaten the King with check positions.
When the King escapes to one of the triangular quadrants, the refuge surfaces are significantly reduced as illustrated in FIG-(H). This allows the opponent to decide which triangular quadrant to attack to capture the King. The FIG-(I) illustrates the Green King in check by the yellow Bishop. FIG-(J) and (K) also illustrate the Green King being attacked by the yellow game pieces and boxed in. The yellow circles are the attack passes of the yellow game pieces and FIG-(K) illustrates the very limited number of spaces to which the King can escape when it is surrounded by the opponent’s game pieces.
While cornering the King to one of the triangular quadrants, another possible strategy is to advance the Pawn to the opponent’s pinnacle. This is an alternative method to win the game rather than capturing the King. As illustrated in FIG-(L) and (M), two Knights on both sides of the Pawn can escort the Pawn to arrive safely to the opponent’s pinnacle.
In the beginning, the Pawns are located on one of the vertex cube surfaces to guard the vertex cubes as illustrated in FIG-(N). In order to access the vertex cube, the opponent player might want to use the Bishop to threaten the Pawn as illustrated in FIG-(O). If the Pawn is captured, the rest of the Pawns are easily under attack by the same Bishop as illustrated in FIG-(P). In order to prevent this, the Green Bishop or the Green Knight can move into certain locations to protect the Green Pawn on the vertex cube as illustrated in FIG-(Q). FIG-(R) illustrates the Green Bishop moving into the position where it can either counter-attack the Yellow Pawn or protects the Green Pawn from the Yellow Bishop which it tries to capture the Green Pawn for the next move. FIG-(S) illustrates the Green Knight's move to guard the Green Pawn just in case the Yellow Bishop attacks during the next move. In conventional chess, the player has to move the Pawn first to free the rest of the game pieces. But in OCTATRIX, the player can move any game piece first, because all game pieces are adjacent to open spaces.
