Proto Prelates

AOF-specific pieces are named...
* after animals with whose heads deities are represented - the Chaturanga Elephant (Alfil);
* after types of mythical creature - the Elf, Gryphon, Simurgh, and Unicorn;
* after religious titles - the Cohen, Druid, Guru, Levite, Magus, Pontiff, Rabbi, and Sadhu;
* after real creatures related to the area continuously through changes in religion - the Camel and Peacock.

The innovation is two further piece types aside, motivated by my extensive use of religious titles as piece names. Many such titles are Christian and are used accordingly in the series, but others such as Guru are more exotic. To include them I added to the two distinguishable pairs of identical sets a fifth set distinguishable from all, with each of its FIDE armies split to represent extra members of two variant armies. The large number of this set's Pawns allows a doubling in the most-bound pieces. This use of pieces gives a case for saying which pairs of armies should use opposite armies of the same sets. Thus the European and Jewish armies should use one psair of sets, here termed Set 1, and the Indian and Persian ones of another pair, here termed Set 2. The set used by all four armies I term Set 3, not unnaturally.

The board is similar to AOF2 but enlarged to 6 levels to make more sense of the increased most-bound pieces and extra piece types. I retain the King's Partner priniciple of one piece aside, able to reach all levels, and a Pawn promotee for everyone - with one substitution of an unbound piece for a bound one. A minor difference is that with so many piece names sharing initials I have expanded to two-letter abbreviations in the array diagram.

Setup

Level 1, King level for the Jewish army, has pieces from that army only. It has no cells in the Indian and Persian Subcamps, which therefore cannot be reached by a direct step or leap from this level.

Level 2, Partner level for the Jewish and Indian armies, has pieces from those armies and the Persian one. It has cells on all columns.

Level 3, King level for the Indian army, has pieces from that army and the Persian one. It has no cells in the Jewish/European Subcamp, which therefore cannot be reached by a direct step or leap from that level.

Level 4, King level for the Persian army, has pieces from that army and the Indian one. It has no cells in the Jewish/European Subcamp, which therefore cannot be reached by a direct step or leap from that level.

Level 5, Partner level for the Persian and European armies, has pieces from those armies and the Indian one. It has cells on all columns.

Level 6, King level for the European army, has pieces from that army only. It has no cells in the Indian and Persian Subcamps, which therefore cannot be reached by a direct step or leap from this level.

Pieces

Kings' Partners:
The FERZ (F_Z) moves one step along any root-2 diagonal, (one level and one column), between opposite corners of any vertical block of 2x2 cells, whose other 2 cells may be empty or occupied but must not be missing. Unlike on 2d and cubic boards a Ferz is unbound (e.g. ed2-fd3-fe2 brings it to an adjacent cell), although as it always switches between odd and even ranks it still cannot return to a cell in an odd number of moves. Initially there is one Ferz, as Indian King's Partner, represented by a Set 3 King, but other players can acquire Ferzes by Pawn promotion. The Ferz was chosen as it has the same r?for both players in Chaturanga. Also notable is its rider the Bishop, not a piece in itself in this game but a component of many. The Bishop makes any number of Ferz steps through empty cells in the same direction, although the board prevents it moving more than 5 steps here. Only the vertical block swept out by each step need be complete, the entire move need not. It always changes level, but may change by an odd or even number of levels.
The FORTNIGHT (F_O) makes r₁₃:1 leaps. This defintion works on both cubic and hex-prism boards, but on a cubic board the r₁₃ coordinate is a Zebra one further expressible as 3:2, whereas here it is an Aurochs one. This means that while a cubic Fortnight can actually triangulate, a hex-prism one always switches between odd and even levels and so cannot return to a cell in an odd number of moves. Again unlike the cubic one, a hex-prism Fortnight is unbound. The cells immediately below the higher, and above the lower, ends of its move may be empty or occupied but must not be missing. Initially there is one Fortnight, as Jewish King's Partner, represented by a Set 3 Queen, whose first move must be to Level 1 (cell fa1, gc1, ie1, or kg1), but other players can acquire Fortnights by Pawn promotion. The name is after a period of two 7-day weeks (see the Jewish-specific Sennight below). Its use for root-14 leapers puns on 14 and the more familiar Knight piece.
The GRYPHON (G_Y) makes one step as the Ferz above (including the need for a complete 2x2 block of cells) but then turns 45? and continues horizontally or vertically as a Rook (requiring only cells along the line to not be missing - or occupied). On this board the whole move must be within a single vertical plane. Initially there is one Gryphon, as European King's Partner, represented by a Set 3 Queen, whose first move must be to Level 5 (cells hb5-cb5 or jd5-ji5), but other players can acquire Gryphons by Pawn promotion. The name is after a creature in European mythology, part bird and part beast, and is long established. The piece played the same r?for both players in Grande Acedrex.
The WAZIR (W) moves one step along any orthogonal, is unbound, and in hex geommetries can triangulate. Initially there is one Wazir, as Persian King's Partner, represented by a Set 3 King, but other players can acquire Wazirs by Pawn promotion. This piece has been widely used in early variants as the Chess concept spread north and west to countries such as Persia, leaving ancient India through territories now in Pakistan such as Waziristan.

European-specific pieces:
The DRUID (D) is the Bishop's compound with the Rumbaba, adding to the Bishop move a single-step move along any hybrid diagonal (one level and and hex-diagonal step). The cells below the upper, and above the lower, ends of the Rumbaba step may be empty or occupied but must not be missing. Like its components it cannot move within a single level. There are 2 Druids, represented by Set 3 Bishops. The name means a priest of an ancient religion of NW Europe.
The ELF (E_F) is a simple root-11 leaper. While this definition on a cubic board equates to a 3:1:1 leaper, here it equates to the r₇:2 leaper - its destination is 2 levels above or below the Sennight's. Both ends of the Sennight moves on both levels must exist. This piece is bound to alternate levels, and cannot reach the Jewish/European Subcamp. As it always moves exactly 2 levels it cannot return to a cell in an odd number of moves. There are 2 Elves, one for odd and one for even levels, represented by Set 1 Queens. The name is of course after a creature in European mythology. Its use for root-11 leapers puns on the modern German for 11.
The PONTIFF (P_F) is the Bishop's compound with the Dicorn, adding to the Bishop move a move of any distance through empty cells along any hybrid diagonal. The need for other cells applies only to each step of the Dicorn move. Like its components it cannot move within a single level. There are 2 Pontiffs, reprtesented by Set 1 Bishops. The name means the chief priest of the established religion of the Roman Empire - a non-Christian one at the time when AOF2 is set.
The UNICORN (U) moves any distance through empty intermediate cells in any of the 6 hex-diagonal directions. Each Unicorn is bound to a third of Level 5 or 6, and can reach no other level. There are 6 Unicorns, to cover all 3 bindings within each level, represented by Set 3 Pawns. The name is of course after a creature in European mythology. My use of it on hex and hex-prism boards extrapolates from the linepiece of the same move lengths on cubic boards.

Indian-specific pieces:
The ELEPHANT (E_T) moves exactly two cells in any of the 12 root-2 diagonal directions. The intermediate cell may be empty, in which case each step of the move must be between opposite ends of a full square of 4 cells, or occupied, in which case the entire move must be between opposite ends of a full square of 9 cells. Each Elephant is bound to one in four cells of all even levels, except in the Jewish/European Subcamp which they cannot reach. As it always moves exactly 2 levels it cannot return to a cell in an odd number of moves. There are 4 Elephants, represented by Set 2 Bishops, to cover all 4 bindings within those levels. It primarily represents elephant-headed deity Ganesh in what was and remains India's largest religion, Hinduism, but elephants are also considered auspicious in, for example, Jainism, another Indian religion surviving from the era.
The GURU (G_U) is a triangulating leaper (like the Gnu). Its components are the 4:1 Giraffe and 5:3 Gimel. It can move 4 levels and 1 column, 4 columns and 1 level, 5 columns and 3 levels, or 5 levels and 3 columns. All are possible within the Drum, and all but the last to or from the Indian and Persian Subcamps, but only the second is available to or from the European/Jewish Subcamp. In all cases it moves between opposite corners of a vertical block, whose other cells may be empty or occupied but must not be missing. It is unbound. There are 2 Gurus, represented by Set 2 Queens. The name is after a kind of holy teacher in various Indian religions. Its use for this piece combines the G and R of Giraffe with a final U for a triangulating compound (e.g. ed2-id1-jd5-ed2 on this board) by analogy with Gnu.
The HARVESTER (H) is the compound of the Bishop and the Anchorite. It makes a Bishop move preceded by an optional orthogonal step and 45? turn. There are 2 Harvesters, represented by Set 3 Knights. The name was coined by Ralph Betza for his Tripunch Chess. As a Bishop compound with a secular name it is used here because I used Hindu titles solely for oblique triangulators.
The SADHU (S_U) is a triangulating leaper (like the Gnu). Its components are the 5:2 Satyr and 7:3 Samel. It can move 5 levels and 2 columns, 5 columns and 2 levels, or 7 columns and 3 levels. All are possible within the Drum, but only the second is available to or from the Indian and Persian Subcamps. In all cases it moves between opposite corners of a vertical block, whose other cells may be empty or occupied but must not be missing. It is unbound except that it cannot reach the European and Jewish Subcamps. There are 2 Sadhus, represented by Set 3 Rooks. The name is after another Indian holy man. Its use for this piece combines the S and A of Satyr with a final U for a triangulating compound by analogy with Gnu.

Jewish-specific pieces:
The COHEN (C_O) moves up to 5 steps along orthogonals or hex diagonals, but never both in the same move, through empty cells, turning either 60° left at each intermediate cell or 60° right at each intermediate cell. As with the Rose inspiring this kind of piece, a move never mixes left and right turns. If there are no 60° turns to make, in this case with a move starting with a vertical step, the move must consist of just that step. There are 2 Cohens, represented by Set 1 Bishops. Its name is a rank in the historic Jewish priesthood. The former spelling is the more familar, but the latter is sometimes used for the ancient priest to distinguish from the surname widespread in modern Jewish society. For knowledge of the ancient meaning I am indebted to Leo Rosten's books on language.
The LEVITE (L_V) is the Bishop's compound with the European-specific Elf - whether in this geometry or in the cubic one. Like its components it cannot move within a single level. There are 2 Levites, represented by Set 3 Bishops. Its name is after a lesser Jewish priest than the Cohen. Its use for this piece is because it shares the first consonant and vowel of Elf, with the intention of extrapolation.
The RABBI (R_A) makes up to 4 steps along hex diagonals through empty cells, turning either 60° left at each intermediate cell or 60° right at each intermediate cell. As with the Rose inspiring this kind of piece, a move never mixes left and right turns. Each Rabbi is bound to a third of Level 1 or 2, and can reach no other level. There are 6 Rabbis, to cover all 3 bindings within each level, represented by Set 3 Pawns. The name is after the most widely-known Jewish religious title. The name has a fairly precise meaning nowadays but was vaguer in the era on which this page is themed. Jewish-Christian ecumenists from both directions sometimes describe Jesus' work of his later life as rabbinical.
The SENNIGHT (S_N) is the root-7 oblique leaper. It moves to the closest cells on the same level that cannot be reached from the same start in a single Rook or Rabbi move, and having reached such a cell goes no further. It cannot be blocked. It is bound to all of Level 1 or 2 and like all pure-hex leapers can triangulate. There are 2 Sennights, one for each level, represented by Set 1 Queens. The name means a seven-day week, which Jews were first to give a major religious significance. Until Christianity became the Roman Empire's official religion, ethnic Jews were the main group observing such a week in Europe. Its use for a root-7 leaper puns on the 7 and the more familiar Knight piece.

Persian-specific pieces:
The CAMEL (C_M) makes 3:1 leaps, that is, between corners of any vertical block of 4x2 cells, whose other 6 cells may be empty or occupied but must not be missing. Unlike on 2d and cubic boards a Camel is unbound (e.g. ed2-fd5-fe2 brings it to an adjacent cell), and as on 2d boards but unlike on cubic ones it cannot return to a cell in an odd number of moves, as it always switches between odd and even levels. There are 2 Camels, represented by Set 3 Knights. It has little to do with the religion of the time, but foreshadows Persia embracing Islam in later history, as a component of my Caliph piece.
The MAGUS (M) is the compound of the Bishop and the Stargazer. It makes a Bishop move preceded by an optional hybrid-diagonal step and 18? turn. There are 2 Magi, represented by Set 3 Rooks. The name is a title in Persian religions, most famously known through the 3 magi said to have been guided to a stable in Roman-era Bethlehem.
The PEACOCK (P_K) moves one step in 14 radial directions: the 4 orthogonals straight up/down/sideways; the 4 root-2 diagonals up-sideways and down-sideways; the 2 hex diagonals straight forward/backward; and the 2 hybrid diagonals combining up/down with forward/backward. Like the King it can triangulate. Peacocks can reach any level but are bound to their player's odd or even ranks. There are four Peacocks, 2 for odd and 2 for even ranks, represented by Set 2 Bishops. Peacocks have a long association with Persian culture, spreading to related religions even beyond the birds' natural habitat - as with the Kurdish "Peacock Angel". Many an ancient Persian stately garden of the kind giving us the word "paradise" would have them as ornamental birds, and Persia's rulers were said to sit on the "Peacock Throne" right up until the name reverted to Iran. It first appears as a piece name as part of a family of mixed-radial hex pieces in my Lengthleaper Hex Chess.
The SIMURGH (S_M) makes one step along a hex diagonal but then turns 30° (but not 90°) and continues as a horizontal Rook. It is bound to all of Level 3 or 4, and cannot reach any other level. There are only 2 Simurghs, represented by Set 2 Queens, even though this is its army's most-bound piece as it is relatively strong and 4 would be give this army too big an advantage. The name is after a creature in Persian mythology, combining a man's head and bird's body, for knowledge of which I must credit 20th-century Dutch artist Maurits Escher. Its use for this piece (and a cubic version) is analogous to the European-specific Gryphon.

Rules

Indian and Persian Pawns have an optional double-step noncapturing move along either horizontal orthogonal (but not one of each) from the starting cell of any Pawn of the same army (including its own). Enemy Pawns of all enemy armies (but no other piece) can capture them En Passant as if they had made only the single step. European and Jewish Pawns have no initial double-step move as they start nearer their promotion cells.

There is no Castling.

A Pawn ending a move on a cell whence it has no unpromoted move must be promoted. Promotion on an enemy piece's starting cell is to the same piece type (but without changing army) as that enemy's King's Partner. Promotion of an Indian or Persian Pawn on an initially empty cell is to one's own King's Partner. Promotion of a European or Jewish Pawn on an initially empty cell is to whichever of Gryphon and Fortnight the player chooses.

A player is Checkmated when their King or Emperor is threatened by the player about to move. That player's pieces are removed from the game and the remaining players then alternate moves starting with the Checkmating one. The Checkmating player's King is promoted to Emperor. The player delivering the third Checkmate wins.

Notes

Although I use the Sennight and hex-prism Fortnight in the same army, it is actually the cubic Fortnight that is the Sennight's dual - that is, its move relates to Ferz steps as the Sennight's does to Wazir moves. Each x+y:x:y cubic piece is the dual of a pure-hex piece.