Silicic acid
Silica Gel
Amorphous Silicon Dioxide
A transparent colloid (gel)
Hydrated silica is the abrasive used in gel toothpastes, or in the clear portion of striped toothpastes. It is often used in opaque toothpastes as well, as a secondary abrasive.
When dried in an oven, hydrated silica looses the water, and becomes a dessicant, a substance that attracts water from the air. You find little packets of "silica gel" crystals in containers whose contents will be damaged by condensing moisture, such as vitamin bottles, consumer electronics, pepperoni, or leather products.
Silica gel can be made by reacting an acid with sodium silicate (sold in drug stores as "water glass" or "egg keep", and used to paint eggs to seal them from air, preventing spoilage). Drying the resulting gel will get the dessicant, or it can be used wet in toothpastes.
You can find sodium silicate in the colorful "Magic Rocks" seen in gift shops at museums. The dry form is mixed with salts of various metals. When you drop them in water, the sodium is replaced by the metal. The resulting metallic silicate is not soluble in water, and has a color characteristic of the metal (e.g. copper is blue). The metallic silicate is also a gel, so it expands, and grows into colorful stalagmites in the water.
hydrated silica: InChI=1/H2O3Si/c1-4(2)3/h1-2H