IGEO7 vs S2

Google's S2 library uses a fundamentally different approach to global gridding: it starts from a cube (not an icosahedron) and produces a hierarchy of quadrilateral cells. This leads to a different set of trade-offs compared to IGEO7.

Overview

Property	IGEO7	S2
Base polyhedron	Icosahedron	Cube
Cell shape	Hexagons + 12 pentagons	Quadrilaterals (near-squares)
Projection	ISEA (equal area)	Tangent/secant sphere–cube
Area variation	0%	up to ~30%
Resolution levels	0–20	0–30
Finest resolution	~2.9 cm (res 20)	~1 cm (level 30)
Index size	64-bit uint	64-bit uint
Hierarchy	Aperture 7	Quadtree (aperture 4)
Pentagons	12 per resolution	None (8 cube corners)
Core library	DGGRID / DGGAL	s2geometry (C++)
Python binding	dggrid4py, pydggal	s2sphere, pys2

Cell Shape: Hexagons vs Quadrilaterals

S2 cells are quadrilaterals — roughly square near the centre of each cube face, increasingly trapezoidal toward edges and corners. IGEO7 cells are hexagons (plus 12 pentagons at icosahedron vertices).

Hexagonal advantages:

All 6 neighbours are equidistant from the cell centre (isotropic neighbourhood)
No preferred axis — hexagonal grids avoid the row/column bias of square grids
Better approximation of a circle for distance-based analyses

Quadrilateral advantages:

Simple 2D addressing (i, j) within each cube face
Natural alignment with raster data (images, DEMs)
Familiar mental model for GIS users

Area Distortion

S2 applies a tangential projection from sphere to cube face, with a non-linear correction function to reduce (but not eliminate) area distortion. The result is approximately ±30% area variation across cells at the same level.

IGEO7's ISEA projection guarantees 0% area variation.

For analyses sensitive to cell size (density, rates, coverage fractions), IGEO7's guarantee is stronger than S2's approximation.

Hierarchy: Quadtree vs Aperture 7

S2 uses a quadtree: each cell subdivides into 4 children. This means:

4× more cells per resolution step (vs 7× for IGEO7)
More resolution levels needed to reach the same physical scale
Each S2 level covers roughly half the linear scale of the previous

IGEO7's aperture-7 steps are coarser (7× per step), so fewer levels span the same range from continental to sub-metre.

Resolution Alignment

IGEO7 res	CLS	Approx. S2 level	S2 avg area
5	~62 km	8	~2,400 km²
7	~8.9 km	11	~300 km²
9	~1.3 km	14	~37 km²
11	~181 m	17	~4,600 m²
14	~9.8 m	23	~18 m²

Note: S2 has 30 levels (0–29) vs IGEO7's 21, reflecting the smaller step size (4× vs 7× per level).

Indexing

Both use 64-bit integers, but the encoding differs:

	IGEO7 Z7	S2 Cell ID
Structure	Base cell + resolution digits	Hilbert curve position
Hierarchy	Explicit digit structure	Implicit in bit pattern
Parent	Truncate last digit	Bit shift
String	2-char base + octal digits	Decimal or token string

S2 Cell IDs encode position along a Hilbert space-filling curve mapped across the cube faces. The hierarchical parent/child relationship is encoded in the trailing bits.

When to Choose IGEO7 vs S2

Choose IGEO7 when:

Zero area distortion is required (density, coverage statistics)
Hexagonal topology is preferred (isotropic neighbourhood)
OGC API DGGS compliance is needed
Integration with DGGRID-based workflows

Choose S2 when:

You need natural alignment with raster/image data (quadrilateral cells)
You are integrating with existing S2-based infrastructure (Google Maps Platform, BigQuery GIS)
Very fine resolution (< 3 cm) is needed (S2 level 30 ≈ 1 cm)
Quadtree spatial indexing suits your data structure

Overview​

Cell Shape: Hexagons vs Quadrilaterals​

Area Distortion​

Hierarchy: Quadtree vs Aperture 7​

Resolution Alignment​

Indexing​

When to Choose IGEO7 vs S2​

Further Reading​