I got an email from Henry Bloomfield which explains the ice cube spikes.
Here it is:


Water is at it's most dense at 4C.


So, if your ice cube freezes very slowly, and the outside freezes before 
the centre, you get freezing water being forced out of a small hole in the
surface as it drops in temperature from 4C to 0C. As it comes into contact
with the cold air in your freezer, it freezes and this is what formes the
'spike' in your picture. The angle and cross-section of the spike are to do
with the arrangement of water molecules in the ice crystal, and indirectly
to do with the angles between the H and O atoms in the water molecule.

End quote. So now we know. Thanks Henry!