Hexagons are six-sided polygons that are used in GIS to apply a uniform grid on a map. In ArcGIS Business Analyst Web App, hexagons are available as a geography option in the smart map search, color-coded maps, and suitability analysis workflows.
H3 hexagons use the open-source hierarchical spatial indexing system, H3, which is commonly used in GIS. Using hexagons in GIS provides a consistent-size grid across an area, unlike using administrative boundaries with varying sizes across an area. The boundaries of hexagons are also consistent over time, unlike administrative boundaries such as block groups or ZIP codes.
Using squares in a grid (or fishnet grid) has been a common GIS practice but is not always preferable since the linearity of squares may inhibit the underlying patterns in the data. Hexagons visually represent curves in the patterns of data and aspects of connectivity or movement paths more naturally than squares. A hexagon grid also suffers less distortion due to the curvature of the earth.
Example
An urban planning organization is analyzing country-wide trends in population density and population growth. The organization is using hexagons in a color-coded map with two different resolutions to analyze areas of highest urban development. The color-coded map is stylized using the Relationship style, which shows two numeric variables in relation to one another. The darker purple indicates both an area of high population density in both 2023 and projected growth in 2028.
Hexagons vary in size (or resolution) from 0 (largest) to 15 (smallest). For country-wide analysis, the organization uses resolution 3 hexagons. This small resolution size produces hexagons that cover a large area and is applicable to country-wide analysis since it provides a broad visualization of data.
There is high population density and projected growth in Illinois that the organization wants to further evaluate. They zoom into the Chicago area and change the hexagons to resolution 6 and add geographic area labels to see which part of the metro area has a high-high relationship. This larger resolution hexagon covers a smaller area per hexagon and is applicable to local analysis since it provides a more specific visualization of data.
For more information on hexagon resolutions, see Hexagon resolutions.
Results
Hexagons are available as a geography option in smart map search, color-coded maps, and suitability analysis. These workflows show the results of the analysis on a map layer and in the Results pane. For more information on the results of these workflows, see the following:
Calculations
Hexagons are six-sided polygons that tessellate. Tessellation is when polygons repeat in a pattern where each unit fits with its neighbor without gaps or overlapping. This continuous pattern allows the curvature of data to be uninterrupted, unlike using squares in a grid on a map.
The shape of the hexagon provides a unique advantage in data analysis and visualization. For instance, a circle can be inscribed within a hexagon. A circle has the lowest perimeter-to-area ratio, which reduces sampling bias, but it cannot tesselate continuously. (A repeating pattern of circles has gaps or overlaps, which is not effective for analysis.) However, a hexagon can tesselate while having a low perimeter-to-area ratio.
The radius of the circle inscribed within the hexagon is called the apothem. The length of the edge of the hexagon is equal on all sides. The apothem and side length of a hexagon are not always equal.
Any point within the hexagon is close to the centroid (or center) of the hexagon because of the obtuse angles within the hexagon. An obtuse angle is an angle that is greater than 90 degrees, whereas an acute angle, like those in a triangle, is less than 90 degrees. Points within polygons that have more acute angles are not close to the centroid. In GIS, centroids are used to convert geographic units, like polygons, into points. The closer a point within a hexagon is to its centroid, the more accurate approximation can be calculated to estimate the distance between polygons.
Note:
For more information on frequently asked questions about H3 hexagons, see Hexagons.
Hexagon resolutions
Hexagons can vary in size, from 0 (largest) to 15 (smallest). The size of the hexagon is referred to as the resolution. Using smaller resolution hexagons (such as resolution 1) is useful for analysis of larger geographic areas, such as country-wide analysis. Bigger resolution hexagons (such as resolution 15) cover a smaller average area per hexagon, resulting in more hexagons covering the same area. For instance, the size of a resolution 1 hexagon is similar in width to the state of Iowa, whereas the size of a resolution 7 hexagon is like LaGuardia Airport.
See the table below for more information on H3 resolution and its corresponding number of cells, average area, and average edge length.
| Resolution | Average hexagon area | Average length of hexagon edge | Average inscribed circle radius (apothem) | |||
|---|---|---|---|---|---|---|
0 | 4,357,449.4 km² | 1,682,420.6 miles² | 1,281.3 km | 796.1 miles | 1,109.60 km | 689.47 miles |
1 | 609,788.4 km² | 235,440.6 miles² | 483.1 km | 300.2 miles | 418.34 km | 259.94 miles |
2 | 86,801.8 km² | 33,514.4 miles² | 182.5 km | 113.4 miles | 158.06 km | 98.21 miles |
3 | 12,393.4 km² | 4,785.1 miles² | 69.0 km | 42.9 miles | 59.74 km | 37.12 miles |
4 | 1,770.3 km² | 683.5 miles² | 26.1 km | 16.2 miles | 22.58 km | 14.03 miles |
5 | 252.9 km² | 97.6 miles² | 9.9 km | 6.1 miles | 8.53 km | 5.30 miles |
6 | 36.1 km² | 13.9 miles² | 3.7 km | 2.3 miles | 3.23 km | 2.00 miles |
7 | 5.2 km² | 2.0 miles² | 1.4 km | 0.9 miles | 1.22 km | 0.76 miles |
Limitations
The limitations for using hexagons include the following:
- ArcGIS Business Analyst Web App provides hexagons as a geography option only for the following workflows:
- Hexagons are only available in the U.S. data sources and the Europe (Beta) data source.
- H3 resolutions 2 through 7 are available per zoom on the map extent.
- If hexagons do not intersect any census blocks, data is not apportioned for them.
- Tabular results using hexagons can be exported to Excel only in the suitability analysis workflow.
Credits
Using hexagons consumes 10 credits per 1,000 map requests (view, pan, and zoom).
See Credits for full information about credit consumption in ArcGIS Business Analyst Web App.
Licensing requirements
Hexagons are available to users with a Business Analyst Web App Advanced license. To learn more about Business Analyst license types, see Licenses.
Resources
For more information on hexagons and using hexagons in ArcGIS Business Analyst Web App, see the following: