Stalactites and stalagmites are neither igneous nor sedimentary. They are secondary mineral deposits formed by the precipitation of minerals from water.

Here's why:

* Igneous rocks are formed from the cooling and solidification of magma or lava.

* Sedimentary rocks are formed from the accumulation and cementation of sediments.

Stalactites and stalagmites, on the other hand, are formed by the following process:

1. Water dissolves minerals from the surrounding rock (often limestone) as it seeps through cracks and crevices.

2. As the water evaporates, the dissolved minerals precipitate out, forming crystals.

3. Over time, these crystals accumulate, forming the familiar shapes of stalactites (hanging from the ceiling) and stalagmites (rising from the floor).

Therefore, stalactites and stalagmites are classified as speleothems, which are secondary mineral deposits formed within caves.