A miraculous voyage

[BMAD]

A traveler just came back from where they observed the most 'miraculous' thing. He visited four small towns in four days. Each town was exactly five miles from each other. Never in his life could he have expected to see four towns that were all the same distance from each other. How was this feat achieved?

[Rob_Gandy]

They were placed in the shape of a tetrahedron.

[bonanova]

vertices of a tetrahedron. one city is on stilts.

[unakade]

But, how can it be a tetrahedron? The cities are just 5 miles away. Any 4 points on the surface of the earth which are also the vertices of a tetrahedron must be at a distance of 1.63 times the radius of the earth (which is about 6500 miles!!!).

[Pickett]

But, how can it be a tetrahedron? The cities are just 5 miles away. Any 4 points on the surface of the earth which are also the vertices of a tetrahedron must be at a distance of 1.63 times the radius of the earth (which is about 6500 miles!!!).

...I'd say he could have visited an asteroid or some other EXTREMELY small body in space to accommodate the shorter distances between towns...The OP doesn't say he was on Earth while doing this trip...

Plus, it truly would be a "miraculous voyage": travel to a small asteroid, land on it safely, find that there are indeed 4 "towns" set up by someone, visit them all, and return back to Earth safely. And never in my life, at least, would I ever expect to see such a thing happen...

So I'll go with that as my answer.

Edited May 17, 2013 by Pickett