Möbius - path of nothingness

In fact, in his 80-plus years, Jodorowsky has had seemingly no idle moments. Born in 1929, he’s been engaged in artistic pursuits in Europe and South America throughout his life. In his early years in Chile, he worked as a mime, clown, and theater director in Santiago. In Paris, he joined Marcel Marceau’s troupe and directed Maurice Chevalier’s music hall comeback. In Mexico City, he founded the Panic Movement with Fernando Arrabal, reviving the spirit of Surrealism with an additional coat of absurdity, and met Ejo Takata, a Buddhist monk who would become his long-term mentor. He also wrote dozens of plays.

A certain construction involving the Möbius-Kantor graph gives an infinite number of connected vertex-transitive graphs that have no Hamilton decomposition (Bryant and Dean 2014).

Following the commentaries, The only map I can imagine from the Möbius strip is the one which send a point $(x,y)$ in the Möbius strip onto $(x,y)$ in $Q$. See the picture below:

Möbius - Path Of NothingnessMöbius - Path Of NothingnessMöbius - Path Of NothingnessMöbius - Path Of Nothingness