The universe of ‘Takuan’s Adventures’ is built as most fairy-tale universes are. It follows the Vedic tradition, where the Universe — Trailokya — is divided into three parts: Urdhva loka (heavens), Madhya Loka (human realm), and Adho Loka (infernal regions).
The Christian Universe follows the same pattern of Heaven, Earth, and Hell. The tripartite structure is also characteristic of the German-Scandinavian cosmogonic geography (Asgard, Midgard, Hel). Greek, Indo-Iranian, Roman, and Celtic cosmologies are all structured in the same way, as shown by Mircea Eliade.
Three worlds are presented in ‘Takuan’s Adventures’ as well: Heavenly, Under, and Earthen Realms. Sometimes Under Realm is referenced as Bottom Realm, and Earthen Realm — as Middle Realm.
If you want to know a little more about the Heavenly, Under, and Earthen Realms, you must visit ‘Universe of Takuan from Koto’ page on Makipedia, the encyclopedia of Anno Ruini.