A5 and the Future of Global Grids: Why Pentagons May Redefine Spatial Indexing
Every decade or so, a new idea emerges that quietly shifts the entire trajectory of geospatial technology. H3 did that for the 2010s. S2 did it before that. But today, we’re looking at something entirely new.
In a conversation with Felix Palmer, creator of A5, I realized just how much latent innovation still exists in something as “solved” as global grids. A5 is a global discrete grid system built on equal-area pentagons, capable of reaching down to 30 square millimeters in resolution. It’s mathematically elegant, visually intuitive, and surprisingly practical.
But maybe the most important part is this: A5 challenges long-held assumptions about how we divide the Earth, encode spatial relationships, and join data efficiently.
This article breaks down why A5 matters, how it works, and where it fits in the future of geospatial analytics.
The Problem With Existing Grid Systems
H3 and S2 have done incredible things for geospatial. They brought indexing, aggregation, and large-scale spatial analytics into the mainstream. But like any abstraction, they come with trade-offs.
And two of those trade-offs have always been difficult to ignore:
1. Unequal Cell Areas
H3 cells vary in size globally. The largest cells are nearly double the size of the smallest.
That means you can’t compare densities between two cities without hidden distortions.
An H3 cell in one region might contain twice the land area of a cell at the same resolution in another region, producing misleading results—especially when aggregating population, listing counts, or environmental indicators.
2. Limited Granularity
H3 bottoms out at around one square meter. That’s fine for rideshare, which was Uber’s original use case. But it’s not nearly enough for satellite imagery, engineering, environmental micro-features, or high-resolution simulations.
Equal area and extreme granularity are core to modern spatial workflows—but historically, you couldn’t have both.
A5 changes that.
Why Pentagons? A New Approach to Global Tiling
A5 isn’t just another grid format. It is built from the ground up on a geometric insight that almost nobody in geospatial had explored.
Felix found a paper from the 1980s describing equilateral convex pentagons that tile a plane. That discovery led to a simple question:
“Why has nobody made a global grid system based on pentagons?”
Pentagons solve a fundamental problem:
- Squares tile a plane, but distort on a sphere
- Hexagons tile locally, but require exceptions (H3 has 12 permanent pentagons)
- Triangles can work, but lead to complex neighbor relationships
Pentagons, surprisingly, give you a tiling that can be projected onto a sphere with no special-case cells. That means uniformity across the entire planet.
The result is a global grid where every cell has the exact same area, with no exceptions—something no other major DGGS has achieved.
True Equal-Area Cells: Why It Matters
Equal area isn’t just a mathematical nicety. It is the foundation for trustworthy spatial analytics.
When Felix showed an example comparing Airbnb density between two cities using H3, the distortion was immediately obvious. H3 made one city appear to have more than double the density of the other. Switching to A5 corrected the comparison entirely.
The difference wasn’t the data—it was the geometry of the cells.
Equal-area grids give you:
- Fair comparisons across regions
- Accurate density calculations
- Better risk scoring
- Cleaner clustering
- Honest heatmaps
- Reliable spatial joins
- Consistent population weighting
If you care about global analytics at scale, this matters a lot.
How A5 Handles Global Coverage and Extreme Granularity
A5 starts with a dodecahedron (a 12-faced shape made of pentagons), then recursively subdivides each face using the pentagonal tiling pattern from the original research Felix found.
Each round of subdivision produces smaller, perfectly equal-area pentagons.
Here’s the surprising part:
A5 can go down to 30 square millimeters.
That’s not a typo. It’s smaller than the tip of your finger.
H3 cannot get anywhere near this level of detail because of the way its indexing scheme is structured. A5’s indexing approach, especially the way it uses a novel space-filling curve, allows nearly unlimited resolution.
A New Space-Filling Curve Designed for Real-World Needs
This is where Felix’s work gets brilliant.
A5 uses a custom space-filling curve that:
- Traverses the world in a continuous, self-similar pattern
- Covers all landmass first
- Leaves oceans for later
That last part is key. Land needs higher resolution. Oceans do not. So A5 allocates more indexing capacity to land to enable the extremely small cell sizes.
This allows the index to represent both:
- Areas (coarse cells)
- Points (cells smaller than a raindrop)
in the same unified framework.
The result is a flexible system capable of replacing many specialized formats.
Why A5 Solves Spatial Joins Better Than Anything Before It
Spatial joins are one of the hardest problems in geospatial analytics.
- Polygons with holes are expensive
- Large geometries are slow
- Different data providers use different boundaries
- Bounding box checks are unreliable
- Global data sets rarely align cleanly
Grid systems solve this by converting every geometry into a set of cell IDs.
Where A5 stands out is in two dimensions:
1. Resolution
Some datasets require meter-level detail. Others require centimeter or millimeter. A5 provides that range.
2. Equal area
Since every A5 cell represents the same area, aggregations are cleaner, more interpretable, and more stable across regions.
That makes A5 a strong candidate for population datasets, climate surfaces, environmental modeling, hazard scoring, infrastructure analytics, and multi-scale analysis.
A5’s Ecosystem: Python, Rust, JavaScript, QGIS, and DeckGL
Felix has done something exceptionally rare:
He shipped working implementations in three languages within months.
- JavaScript
- Python
- Rust
He used large language models to translate and test the implementations, uncovering precision issues that only surfaced when writing in a different language.
This made the entire codebase more accurate.
Today, A5 already has:
- A Python library
- A Rust library
- A JavaScript library
- Integration with vGrid
- A brand-new QGIS plugin
- A dedicated DeckGL layer coming in version 9.2
That ecosystem is growing faster than any DGGS I’ve seen in years.
Practical Use Cases for A5
If you’re wondering where A5 fits into real workflows, start here:
Population Density and Demographics
Equal-area cells mean density calculations are truly comparable worldwide.
Climate Surfaces and Environmental Indicators
High granularity supports fine-grained environmental layers like surface temperature, NDVI, air quality, or microclimate zones.
Mobility, Transportation, and Logistics
Stable indexing simplifies cross-city comparisons and network modeling.
Remote Sensing and Satellite Imagery
30 mm cells allow pixel-precise indexing for high-resolution imagery.
Disaster Risk, Insurance, and Hazards
Global uniformity eliminates distortion in risk scoring models.
Data Providers
Publish once in A5 and unlock compatibility across tools instantly.
Where A5 Is Going Next
Felix is continuing to refine:
- The core library
- The API surface
- Documentation
- Cross-language consistency
- Visualization support
- Academic validation
But the biggest request is simple:
He wants people to start using A5—testing it, building on top of it, and pushing it into real-world problems.
The next generation of DGGSs will not be shaped by geometry alone. They will be shaped by adoption, accessibility, data provider support, and ecosystem growth.
A5 is positioned to be one of those systems.
Conclusion
A5 bridges something rare in geospatial:
mathematical elegance and real-world utility.
Equal-area pentagons.
Global coverage.
Extreme granularity.
A flexible indexing scheme.
A fast-growing ecosystem.
And a clear set of advantages over existing DGGSs.
It’s the kind of innovation that reminds us how much room remains for progress in the fundamentals of geospatial computing.
If you’re a data scientist, researcher, engineer, or data provider, now is the perfect time to experiment with A5. This is one of those technologies that quietly grows from niche curiosity to a foundational building block.
And in a few years, we may look back and wonder how we ever lived without equal-area pentagons.
