My new corian sink has spider cracks in the basin and I want to know two things: how to repair the cracks and what causes the cracks. Out of three sinks, only one of the basins is free from cracks. Thanks

Officially, from DuPont, there is no repair. However, This works very well:

https://sites.google.com/site/coriartinc/Home/price-list/simple-permanent-crack-repair

As to the cause: The cracks are caused by repeatedly pouring boiling water directly into the sink. You should have the cold water running when doing this.