There are some clocks, mostly in or around international airports, which have multiple faces to show the time at various cities around the world. Taking more a forward-looking approach is [Chronova Engineering], who built a clock to display the time on four different planets: Earth, Mars, Jupiter, and Saturn.
The clock doesn’t have any hands, but it uses rotating dials to represent a top-down view of each planet from it’s north pole. The dials have degree markings to represent rotation relative to each planet’s prime meridian; for the gas giants, rotation is measured by the rotation of the planet’s core. Each dial’s center is made out of a circular stone tile with patterns similar to those seen on the planet; Earth, for example, is represented with sodalite. Three pointers mounted around the dial indicate the longitudes which are currently experiencing sunrise, noon, and sunset. The mechanism can be turned with a handle or a knob, and a mechanical counter keeps track of the number of Earth days that have passed.
[Chronova] machined most of the mechanism out of brass, with a few steel parts. It required only nine gears, including the two idler gears which were used to space out the dials and keep them rotating in the right direction. The gears were machined on a jeweler’s lathe, with the cutouts in the idler gears being made with a pantograph milling machine and a 3D printed pattern. This isn’t technically a clock, since there’s no timekeeping mechanism, but it does accurately represent relative motion.
Though they represent different things, this project is reminiscent of an orrery, which [Chronova Engineering] has previously built. For more detail about the difficulties of synchronizing time between celestial bodies, check out this article about establishing a lunar time standard.

“built a clock to display the time on four different planets”
Add to that the obvious question “The time where on the four different planets?”
“This isn’t technically a clock, since there’s no timekeeping mechanism”
You can understand my confusion.
It shows the time on the whole planet, since it’s more of a “rotation cycle phase” display than it is a clock.