# H3 Index Representations

## Introduction

The H3 system assigns a unique hierarchical index to each cell. The H3 index of a resolution r cell begins with the appropriate resolution 0 base cell number. This is followed by a sequence of r digits 0-6, where each ith digit di specifies one of the 7 cells centered on the cell indicated by the coarser resolution digits d1 through di-1. A local hexagon coordinate system is assigned to each of the resolution 0 base cells and is used to orient all hierarchical indexing child cells of that base cell. The assignment of digits 0-6 at each resolution uses a Central Place Indexing arrangement (see Sahr, 2014). In the case of the 12 pentagonal cells the indexing hierarchy produced by sub-digit 1 is removed at all resolutions.

Child hexagons are linearly smaller than their parent hexagons.

## H3Index Representation

The H3Index is the integer representation of an H3 index, which can be placed into multiple modes to indicate the concept being indexed.

• Mode 1 is an H3 Cell (Hexagon/Pentagon) index.
• Mode 2 is an H3 Unidirectional Edge (Cell A -> Cell B) index.
• Mode 3 is planned to be a bidirectional edge (Cell A <-> Cell B).
• Mode 0 is reserved and indicates an invalid H3 index.

• This mode remains, partially, for backwards compatibility with an older version of H3.

Mode 0 contains a special index, H3_NULL, which is unique: it is bit-equivalent to 0. This index indicates, specifically, an invalid, missing, or uninitialized H3 index; it is analogous to NaN in floating point. It should be used instead of an arbitrary Mode 0 index, due to its uniqueness and easy identifiability.

The components of the H3 cell index (mode 1) are packed into a 64-bit integer in order, highest bit first, as follows:

• 1 bit reserved and set to 0,
• 4 bits to indicate the index mode,
• 3 bits reserved and set to 0,
• 4 bits to indicate the cell resolution 0-15,
• 7 bits to indicate the base cell 0-121, and
• 3 bits to indicate each subsequent digit 0-6 from resolution 1 up to the resolution of the cell (45 bits total are reserved for resolutions 1-15)

The components of the H3 unidirectional edge index (mode 2) are packed into a 64-bit integer in order, highest bit first, as follows:

• 1 bit reserved and set to 0,
• 4 bits to indicate the index mode,
• 3 bits to indicate the edge 1-6 of the cell to traverse,
• 4 bits to indicate the cell resolution 0-15,
• 7 bits to indicate the base cell 0-121, and
• 3 bits to indicate each subsequent digit 0-6 from resolution 1 up to the resolution of the cell (45 bits total are reserved for resolutions 1-15)

The canonical string representation of an H3Index is the hexadecimal representation of the integer, using lowercase letters. The string representation is variable length (no zero padding) and is not prefixed or suffixed.

The three bits for each unused digit are set to 7.

## Bit layout of H3Index

The layout of an H3Index is shown below in table form. The interpretation of the "Reserved/edge" field differs depending on the mode of the index.

0x0F 0x0E 0x0D 0x0C 0x0B 0x0A 0x09 0x08 0x07 0x06 0x05 0x04 0x03 0x02 0x01 0x00
0x30 Reserved Mode Reserved/edge Resolution Base cell
0x20 Base cell Digit 1 Digit 2 Digit 3 Digit 4 Digit 5
0x10 Digit 5 Digit 6 Digit 7 Digit 8 Digit 9 Digit 10
0x00 Digit 10 Digit 11 Digit 12 Digit 13 Digit 14 Digit 15