We had a large upwards icicle in our backyard. This is similar to a stalagmite, but it's formed in a different way. Sometimes when water freezes, some of the water pushes through an unfrozen patch and freezes as it goes, forming an upwards spike. You see these in plastic ice cube trays sometimes. An article in New Scientist said that you only see these with plastic containers. Out thermometer said it was minus 4 C, when we first saw the icicle in the morning.
Upsidedown Growing Icicle