The .thumbnails Directory
To not hide the generated thumbnails in obscure directories and thus don't make them locateable for the user, the directory for storing the thumbnails is named .thumbnails and located in the users home directory.
The Directory Structure
Since this standard supports different thumbnail sizes (see 'Thumbnail Size' section) there are multiple subdirectories within the .thumbnails directory. Most of these follow the nameing scheme 'width'x'height', which means that all thumbnails stored in these directories are 'width' pixels wide and 'height' pixels tall. The 'fail' directory will be discussed in the Thumbnail Generation Failure section:
.thumbnails/
.thumbnails/48x48/
.thumbnails/64x64/
.thumbnails/96x96/
.thumbnails/128x128/
.thumbnails/160x160/
.thumbnails/192x192/
.thumbnails/fail/
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With this structure you can find all medium sized thumbnails in the 96x96 directory.
 | The number of thumbnail sizes and the sizes themselves are preliminary. There need to be some more discussion about sensible values. |