# Irregular grids

Here are some types of irregular grids common in WPC-style puzzles.

## Unusual partition[edit]

In some puzzles, the geometry used in it is conventional square one, but the cells are partitioned differently.

**Row/Column**: The same as normal square grids. For example, this is Irregular Kakuro from WPC 2016 IB.

## Hexagonal[edit]

Examples of originally hexagonal puzzles include Boomerangs.

**Row/Column**: Translated into 3 directions. For example, this is hexagonal Easy as AB from PGP IB.

**Straight/Right Turn**: Some puzzle forbids 60° turns at all. Some puzzle introduces a different notation for loop being straight, making 60° turn, making 120° turn.

**2x2-Constraint**: Traslated into no "triangles" (three cells adjacent to each other) being completely shaded. For example, this is hexagonal Nurikabe from WPC 2019 IB.

## Triangular[edit]

**Triangular**: Translated into 3 directions. For example, this is triangular Lighthouses from WPC 2019 IB.

**Straight/Right Turn**: Loop makes 120° turn in every cells.

## Pyramidal[edit]

Geometrically identical to hexagonal grids, but the overall shape of the grid is triangular. An example of originally pyramidal puzzles are Pyramid and Trid.

## Cairo Pentagonal[edit]

**Row/Column**: Undefined, since there are no straight direction.

**Straight/Right Turn**: Translated into: "when edges that the loop crosses when entering and leaving the cell are adjacent, the loop "makes a turn" in the cell." This is Cairo Pentagonal Masyu from WPC 2019 IB.

**2x2-Constraint**: Translated into; No interior point is completely surrounded with black cells. For example, this is Cairo Pentagonal Nanro Signpost from WPC 2019 IB.

## General Graph[edit]

If the puzzle rules only require the concept of edgewise connectivity, then the puzzle can be presented on any graph. For example this is "3D" Fillomino from WPC 2019 IB.

## Cylindrical, Toroidal, Möbius strip[edit]

In a **cylindrical** grid, the leftmost and the rightmost columns (or the topmost and the bottommost rows) are considered adjacent.

In a **toroidal** grid, the topmost and bottom rows and the leftmost and the rightmost columns are respectively considered adjacent. For example, this is a toroidal Snake from WPC 2019 IB.

In a **Möbius strip** grid, the topmost cell of the leftmost column is connected to the bottom cell of the rightmost column, et cetera.