Well almost perfect dome - in 1528 the mosque & tomb of Jamali Kamali's was built. And this shows the top portion where they were able to support the dome by adding extra quinches. If you see in between the top side arch and centre one there is an extra bar.
However with these mathematical quinches add ons( 8 /16/32) gave the shape of domes as ONION Tops.They were not perfectly round.
Building tombs - generally when we rest a body for final peace - they should have the open sky facing them, so why the tombs were built ?
Everyone gets succumbed to that feeling of " How to get to the level of Immortal stage" - architecture is one such way to inspire awe . However closed confines of a building would have meant going against the teachings of religion. So if you stand inside the tomb and see upwards -you do get the sense of vastness. Then they use to have star and moon crecent carved so it was like facing the open sky.
And last trivia - most of the tombs were started before their actual death... so basically these rulers were seeing their grave site being dug in front of them.... ( whow- at this my jaw dropped...) and on serious note - if some overzealous fan comes and tell you that he would like to build " Taj Mahal" for you - do not feel flattered :-)