Calcite is composed of calcium ions (Ca) and carbonate ions (CO3). In it purest form, calcite is transparent with rhombic shaped faces with a glassy luster. Calcite is relatively soft and has good clevage along three directions.

One popular type of calcite is called Iceland spar which is common in fractures and cavities in basalt. It has a very easily identifiable property known as double refraction. When you place a piece of Iceland spar on text, you can see the text twice through the crystal.

Information provided by Patrick M. Colgan, Northeastern University
http://www.casdn.neu.edu