# Irregular grids

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

## Unusual partition

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

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

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

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

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

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

In a cylindrical grid, the leftmost and the rightmost rows are considered adjacent.

In a toroidal grid, the topmost and bottom rows and the leftmost and the rightmost rows 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 row are connected to the bottom cell of the rightmost row, et cetera.