Spherical Chess
Spherical Chess is a family of chess variants adapted to spherical topology — a surface with no edges, where all directions eventually curve back to their origin. Multiple independent inventors have designed spherical chess between 1950 and 2014. The variants share a common framework but differ in how the Bishop and Knight handle the polar singularities.
The Board and Topology
Spherical Chess is played on a standard 8×8 board, but the board is conceived as a sphere:
Horizontal wrap (as in Cylindrical Chess): Ranks loop back into themselves. The a-file connects to the h-file — a Rook moving right off the h-file reappears on the a-file at the same rank.
Polar wrap: The board does not wrap vertically in a simple torus manner. Instead, files are treated as lines of longitude that meet at the poles (rank 1 and rank 8). When a piece crosses a pole:
- A Rook moving forward off rank 8 continues from rank 8 on the file four files away (e.g., Ra3-a1-e1-e4)
- The shift is always exactly 4 files (half the board width)
This means:
- There are no edge squares — every rank wraps
- There are no corner squares — the poles are where all files converge
- Pieces near the poles have reduced move counts (fewer unique destination squares)
Piece Movement Near the Poles
Rook: Crosses the pole by continuing 4 files away on the same rank, then continues moving away from the pole. Example: Ra3 → a2 → a1 (pole crossed) → e1 → e2 → e3…
Bishop (most versions): Crosses the pole and continues on the same diagonal colour (colourbound). Moving diagonally into the pole, it exits directly across, then reverses its diag direction. The exact rule differs by version:
| Version | Transpolar Bishop rule |
|---|---|
| Grayber/Miller (1950s/1965) | Complex zig-zag; not colourbound |
| Yapsan (1971) | Crosses directly across pole (same file shifted 4); colourbound; reverses direction |
| Nadvorney (1975) | Shifts 3 files (not 4), changes colour; complex path |
| Boholy/Welman/Chao (1987–2008) | Same as Yapsan; colourbound |
The majority of versions (Yapsan, Boholy, Global Chess, Chess on the Dot) use the Yapsan-style colourbound Bishop: crosses the pole directly 4 files away, reverses diagonal direction, stays on the same colour.
Knight: In most versions (Yapsan, Nadvorney, Global Chess, Chao), the Knight has exactly 8 possible moves from any position on the board, including those near the poles, by applying the L-shaped leap with polar adjustment.
King and Queen: Move as derived from Rook and Bishop above. King near a pole has 6 possible moves (not 8).
Pawn: Moves as in Cylindrical Chess — forward only, no trans-polar movement until promotion.
Castling
In the Yapsan, Nadvorney, and Chao versions, two extra castling options are available: the King may castle with a Rook by approaching it from either side (not just the standard approach). The usual castling conditions must still be met.
Key Versions
| Year | Inventor | Key feature |
|---|---|---|
| 1950s | H. D. Grayber | First documented; complex non-colourbound Bishop |
| 1965 | Don Miller | Knight near pole gains extra move (8 moves) |
| 1971 | Peter Yapsan | Colourbound Bishop; 8-move Knight; extra castling |
| 1975 | Leo Nadvorney | Bishop changes colour at pole; 8-move Knight |
| 1987 | János Boholy | Pole is a neutral passing space; 6-move Knight near pole |
| 1989 | Welman & Welman | Global Chess; 8-move Knight (orig.); later reduced |
| 2008 | Joshua Chao | Chess on the Dot; Yapsan-style; forbids stationary moves |
Rules
- Standard FIDE starting position
- Standard FIDE rules apply, except as modified by spherical topology
- No stationary moves (pieces may not make a complete loop and return to their starting square) — in most versions
- Win: Checkmate
Attribution
Spherical Chess is a family of chess variants invented independently multiple times between 1950 and 2014. Surveyed by Fergus Duniho. Source: chessvariants.com/boardrules.dir/spherical.html (last modified July 29, 2021).