Polyknight
Figure formed by knights moves on a grid
A polyknight is a plane geometric figure formed by selecting cells in a square lattice that could represent the path of a chess knight in which doubling back is allowed. It is a polyform with square cells which are not necessarily connected, comparable to the polyking. Alternatively, it can be interpreted as a connected subset of the vertices of a knight's graph, a graph formed by connecting pairs of lattice squares that are a knight's move apart.
Enumeration of polyknights
Free, one-sided, and fixed polyknights
Three common ways of distinguishing polyominoes for enumeration can also be extended to polyknights:
free polyknights are distinct when none is a rigid transformation (translation, rotation, reflection or glide reflection) of another (pieces that can be picked up and flipped over).
one-sided polyknights are distinct when none is a translation or rotation of another (pieces that cannot be flipped over).
fixed polyknights are distinct when none is a translation of another (pieces that can be neither flipped nor rotated).
The following table shows the numbers of polyknights of various types with n cells.
This brief starts where responsible research should: with the source description of “Polyknight” as figure formed by knights moves on a grid. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as figure formed by knights moves on a grid. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 21, 2025. The linked authority identifier is Q7226514. None of the 0 selected statements returned an explicit reference.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
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This entry incorporates text from “Polyknight” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.