## Pieces[edit | edit source]

There are eight likely chess pieces with full octahedral symmetry. (Nine including the king.)
Possible pieces with less symmetry are pyritohedron and tetrahedron, which both come in two different orientations.
Octahedron and tetrahedron can reach only a quarter of the fields.

There are two kinds of diagonal (square and cube), so one might define two kinds of pawns, as well as their combination.
To fill the second plane with cheap cover, one may add a weak pawn, that captures only forward (and might even die when it captures).

basic pieces

|  |
|  | (0, 0, 1)
cube
rook

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|  | (0, 1, 1)
rhombic dodecahedron
bishop (colorbound)

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|  | (1, 1, 1)
octahedron
councillor

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combinations

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|  | small rhombicuboctahedron
queen

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|  | great rhombicuboctahedron
king

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|  | cuboctahedron
marshal

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jumpers (knight like pieces)

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|  | (0, 1, 2)
tetrakis hexahedron
knight

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|  | (1, 1, 2)
deltoidal icositetrahedron*
jester (colorbound)

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|  | (1, 2, 2)
triakis octahedron*
archer

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Target points form a truncated octahedron. |
Target points form a rhombicuboctahedron*. |
Target points form a truncated cube*.
half pieces

|  |  |
|  |  | pyritohedra (half of tetrakis hexahedron)
guard

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|  |  | tetrahedra (half of octahedron)
scribe

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Target points form an icosahedron*.
pawns

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|  | front  |

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|  | square diagonal  |

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|  | cube diagonal  |

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|  | both diagonals  |

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## Space (board)[edit | edit source]

An 8×8×8 cube (with 512 fields) would probably be too big. A 6×6×6 cube (with 216 fields) or 6×6×8 cuboid (with 288 fields) seem reasonable.

### Possible starting positions[edit | edit source]

It seems reasonable, that every piece in the first plane, except queen and king, should exist twice. That would be 20 pieces.
The arrangement below is one example how that could look. It is not yet tested.
Only half the fields can be reached by octahedra, and the other half by tetrahedra.
If the black positions are mirrored, no green pieces of the same type can threaten each other (but octahedra and tetrahedra can).

white polyhedra

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white pawns

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black pawns

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black polyhedra

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