# Determine the latitude/longitude coordinates of the center point of an H3Index cell

This operation is performed by function `cellToLatLng`

. See the comments in the function source code for more detail.

The conversion is performed as a series of coordinate system conversions described below. See the page Coordinate Systems used by the H3 Core Library for more information on each of these coordinate systems.

- The function
`_h3ToFaceIjk`

then converts the H3 index to the appropriate icosahedron face number and normalized*ijk*coordinate's on that face's coordinate system as follows:

- We start by assuming that the cell center point falls on the same icosahedron face as its base cell.
- It is possible that the cell center point lies on an adjacent face (termed an
*overage*in the code), in which case we would need to use a projection centered on that adjacent face instead. We recall that normalized*ijk*coordinates have at most two non-zero components, and that in a face-centered Class II system the sum of those components is a resolution-specific constant value for cells that lie on the edge of that icosahedral face. We determine whether an overage exists by taking the sum of the*ijk*components, and if there is an overage the positive*ijk*components indicate which adjacent face the cell center lies on. A lookup operation is then performed to find the appropriate rotation and translation to transform the*ijk*coordinates into the adjacent face-centered*ijk*system.

- The face-centered
*ijk*coordinates are then converted into corresponding*Hex2d*coordinates using the function`_ijkToHex2d`

. - The function
`_hex2dToGeo`

takes the*Hex2d*coordinates and scales them into face-centered gnomonic coordinates, and then performs an inverse gnomonic projection to get the latitude/longitude coordinates.