Board Hex Axial Neighborhood

Enumerate six infinite axial hex-grid neighbors in a fixed direction order; no board clipping or geographic coordinates.

Description

Enumerate six infinite axial hex-grid neighbors in a fixed direction order; no board clipping or geographic coordinates.

A hex cell has six axial neighbors under the declared q/r convention.

When to use this tool

Enumerate six infinite axial hex-grid neighbors in a fixed direction order; no board clipping or geographic coordinates.

Prepare the supplied q, r fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter q, r. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.neighbors. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Add offsets (1,0), (1,-1), (0,-1), (-1,0), (-1,1) and (0,1) to the supplied integer q/r pair, in that order.^[1]

Input field	Meaning and representation	Accepted input
q	q.	Integer from -1e9 to 1e9 inclusive
r	r.	Integer from -1e9 to 1e9 inclusive

Output field	Interpretation
result	Object containing the named outputs below.
result.neighbors	The neighbors list in the ordering and representation described above.

json

{
  "input": {
    "q": 0,
    "r": 0
  },
  "output": {
    "result": {
      "neighbors": [
        [
          1,
          0
        ],
        [
          1,
          -1
        ],
        [
          0,
          -1
        ],
        [
          -1,
          0
        ],
        [
          -1,
          1
        ],
        [
          0,
          1
        ]
      ]
    }
  }
}

Limitations and assumptions

The grid is unbounded. No blocked cells, wrapping, terrain or board clipping is considered.
Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.

Alternative or Complementary methods

Use a game-state-aware rules engine when occupancy, legal moves or scoring rules matter. These operations calculate coordinates, local geometry or supplied ledger totals without inferring a complete position.

References

Tool behavior and example: Board Hex Axial Neighborhood — tool.io

Similar or alternative tools

Board Hex Axial Cube Converter
Convert integer axial hex coordinates q,r to cube x=q,z=r,y=-q-r, preserving the zero-sum invariant.
Board Hex Cube Axial Converter
Convert validated zero-sum integer hex cube coordinates to axial q=x,r=z; invalid cube coordinates are rejected.