It is likely that you will use axial or offset coordinates in your project, but many algorithms are simpler to express in axial/cube coordinates. Either choose to store the s coordinate (cube), or calculate it when needed as - q- r (axial). For maps with rotation, or non-rectangularly shaped maps, use axial/cube. My recommendation: if you are only going to use non-rotated rectangular maps, consider the doubled or offset system that matches your map orientation. * rectangular maps require an adapter, shown in the map storage section They seem potentially useful for fixed sized hexagonal shaped maps. See this question or this question on stackoverflow, or this paper about machine vision, or this diagram about "generalized balanced ternary" coordinates, or this math paper, or this discussion on reddit. There are spiral coordinate systems I haven't explored. One of the interesting properties of that system is that it reveals hexagonal directions. There are also cube systems that use q-r, r-s, s-q. Some have the 120° axis separation as shown here and some have a 60° axis separation. There are also many different valid axial hex coordinate systems, found by using reflections and rotations. Some of them have constraints other than q + r + s = 0. There are many different valid cube hex coordinate systems. To avoid confusion in this document, I'll use the names q r s for hexagonal coordinates (with the constraint q + r + s = 0), and I'll use the names x y z for cartesian coordinates. In previous versions of this document, I used x z y for hexagonal coordinates and also for cartesian coordinates, and then I also used q r s for hexagonal coordinates. If you have any references, please send them to me. Tamás Kenéz sent me the core algorithms (neighbors, distances, etc.). Other possible names: brick or checkerboard. I haven't found much information about this system - called it interlaced, rot.js calls it double width, and this paper calls it rectangular. The constraint is that q + r + s = 0 so the algorithms must preserve that. The cube coordinates are a reasonable choice for a hex grid coordinate system. We'll use this property in the neighbors section. For example, northwest on the hex grid lies between the +s and -r, so every step northwest involves adding 1 to s and subtracting 1 from r. Each direction on the hex grid is a combination of two directions on the cube grid.Try the same for q (green) and s (purple). Try highlighting a hex with r at 0, 1, 2, 3 to see how these are related. Each direction on the cube grid corresponds to a line on the hex grid.Selecting the hexes will highlight the cube coordinates corresponding to the three axes. Study how the cube coordinates work on the hex grid. Shoves even columns down Cube coordinates #