I You are correct with your voltages except on the the center grounded delta system you will get 416 volts on the high leg, it is 216 volts on a 240/ 120 volt system.So, you're saying mathematics is incorrect?
I don't know what measuring line-to-line voltages has to do with line-to-neutral voltages.
I have extensive practical knowledge. I'm an industrial electrician and have been working with, and studying 3 phase power systems nearly 30 years.
So it's true for everyone but you? Seems to me you're the one having difficulty understanding!
Note that there are two kinds of 3 phase distribution systems: wye and delta. For systems where a neutral is used, the wye is more common since it allows for the possibility of a balanced system, whereas a grounded delta system (be it corner-grounded or center-grounded) will be unbalanced by design.
In the case of a center-grounded delta system, the line-to-neutral voltage readings from 2 of the phases will result in half the line-to-line voltage (that is, 240V line-to-neutral on a 480V system). However, the 3rd leg will measure approximately 208V to neutral.
On a grounded 480V wye system, the line-to-line voltages will, of course, measure 480V. But measure any one of the phases to neutral, and you will see that it is 277V, not 240V.
If you're getting something other than these readings, you're either doing something wrong, or you have a bad meter.