When the tiles are laid out in this manner it is called the Symbolic Square of Mah Jongg. With this symmetrical type of display, you are able to see all 144 tiles of the set. You will note that the Symbolic Square is designed for sets used for Chinese mahjong, not for American Mah Jongg, as there are no Jokers.
Here is another Mah Jongg set displayed as a Symbolic Square:
This is truly a beautiful way to display the tiles of your vintage sets.
Thanks to Peter Gregory and Mahjong British Rules.