Our Canadian office managed to convince a couple of team members in our American office that we ran on a 20 hour clock, with 72 minutes in an hour. That was fun for a week.
So he wrote a digital clock that used standard-length seconds, but 70 of them per minute, 60 of those minutes per hour, and 24 of those hours per day. So when it was 10:30:59 by his nonstandard clock, he was at the phase of his nonstandard day that corresponds to 10:30 or so of the standard day --- but the clock would then roll over to 10:30:60, 10:30:61, ... 10:30:69, 10:31:00.
It was very amusing to see people's reactions upon watching the clock for a little while, especially at the time of week that it was more or less in phase with normal time.