Little Star

This is the tiny flower of a favorite succulent.  It's difficult to get photos because the flowers appear almost at the base of the stems, which cluster together at soil level. The stems are long and hang down over the sides of the pots, and when my husband was sweeping the porch he accidentally broke one off. Lo and behold there was a flower on it! He stuck it in the soil of another pot, at the correct angle for a photo! 
I don't know the name of this plant - if someone out there know, please tell me!