Area

An area is any orthogonally contiguous subset of a grid that is demarcated, such as with a different color, but which is not delineated (and hence is not a region).

Bar

A bar is a group of continguous cells in a single rank.

Cage

An irregularly shaped area, either a region or an area.

Cell

A cell is any single area of a grid-based puzzle. In square and rectangular grids, cells are the smallest squares in the grid.

Diagonal neighbors

Two cells are diagonal neighbors if they touch at exactly one point (that is, they are neighbors but not orthogonal neighbors).

Edge

An edge is the side of a cell.

House

Any subset of the grid that must contain the full complement of values, such as (in sudoku) a row, a column, or a region.

Incomplete Latin Square

A Latin Square is incomplete if some of the cells are blacked out, but the remaining cells otherwise form a Latin Square.

Island

An island is any orthogonally contiguous subset of a grid that is not orthogonal to the grid's outer border.

Jordan Curve

A Jordan curve is a closed, non-intersecting loop, consisting of segments. A region which does not contain any islands is bounded by a Jordan curve.

Latin Square

A grid forms a Latin square if no digit appears twice in any row or column.

Line

A line consists of one or more joined segments.

Manhattan Distance

The Manhattan distance is the minimum number of orthogonal neighbors between two cells, not including the cells themselves.

Neighbors

Two cells are neighbors if they touch at any point.

Nonet

A 3x3 region in a standard sudoku puzzle.

Ocean

If a puzzle has islands or peninsulas, then the remaining cells comprise the ocean.

Orthogonal neighbors

Two cells are orthogonal neighbors if they share a side. In a square grid, this means that they are in the same row or column.

Orthogonally contiguous

An area is orthogonally contiguous if it is possible to move from any cell in the area to any other cell by travelling only through orthogonal neighbors within the area.

Peninsula

A peninsula is any orthogonally contiguous subset of a grid that is orthogonal to the grid's outer border.

Rank

A rank is any row or a column.

Region

A region is any orthogonally contiguous subset of a grid that is delineated by a line. For instance, a standard 9x9 Sudoku grid contains nine regions, which are 3x3 squares.

Rotational symmetry

Symmetry based on rotating the shape around a center point.

Segment

A segment is a solid straight line.

Ship

A bar (in a puzzle using an ocean metaphor).

Terminal

A terminal represents one end of a line.

Terminal point

In certain puzzles, the initial clues consist of a set of points that act as terminals in the solution.

Wall

A wall is a segment between two adjacent cells.