Answer :

Stalactites hang downwards from the ceiling and are form by crystalizing water dropping down.

Stalagmites are formed similarly by dropping water, but they seem to grow up from the ground. They are like triangular pillars coming out of the ground. 

Sometimes those two can, by being formed a the same period of time, create a column which would be thinner in the middle and thicker both, near the ground and the ceiling.