Box Dot is originally designed as a character paper toy by Graphig (グラフィグ).
As the name implies, the design features a chibi, cutesy style character in a boxy, square shape, and the characters sitting down facing diagonally to the right.
The design then became popular and widely spreaded on Twitter with the making of the design by Hanaya (花屋) published on his/her blog.
Currently, all materials and template can be found on his/her blog site, along with the instructions and making of the design as well. For those who are interested, you can visit the blog site to find out how to make your own Box Dot for your icon.
MM • 箱ドットまとめ… Materials and Other Compilations (Japanese only)