Consider a mostly 2D game which takes place on a large cubical world. When crossing over to another face, the in-game time of day changes by 6 hours, as does the position of the sun in the sky (if it is 2.5D like Minecraft).
We leave unspecified exactly what the user experience is near a face boundary. Maybe a cutscene. Or towers.
We have assumed the cubical world consists of 2 square polar regions and an equatorial belt of 4 squares. Unclear what time zone the polar regions should be. Probably just divide each into 4. It's always twilight in the polar regions, unless we model axis tilt.
Or, orient the cube with vertices at the poles: 6 diamond-shaped regions (which might not work so well with a rectangular screen). Each diamond is its own time zone: 4 hours each. It's possible to travel in an oblique slant such that time changes the opposite way compared to if time zone boundaries were straight north-south (kind of like the unusual orientation of the Panama Canal).
Could do any polyhedron. Each face is a time zone.
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