The meaning of the word Linga is that which indicates. The Shiva Linga that is visible after the installation is the top one third and the other two third forms the base.
The first one third of the base stands for Brahma - the aspect of creation in the cosmos. As the creation brings things into the existance, naturally the process is directed outward (i.e. towards the object of creation). Since the creation is going on endlessly, the four directions represent this concept. One can move in each direction without reaching the end. This aspect of the Lord is called Brahma - the Lord as the Creator and is represnted by the square cross section standing for four directions.
The middle one third represents Vishnu - the one that pervades everything in the creation. The four directions and four corners totalling to eight along with up and down directions cover everything and it is indicated by the octagonal middle cross section.
The top one third represnts the Shiva aspect by the circular cross section indicating the Limitlessness. Though there are three aspects indicated, the Shiva Linga is one alone and when worshiped all three inseparable aspects are worshiped.
Thus SHIVA and VISHNU are no two different entities!! It is one Limitlessness viewed from different aspects so mind has a direction to contemplate. Vishnu is also worshipped and invoked in the form of Shaligrama (a spherical shape) standing for the Limitlessness as so is Shiva...
Since this information and understanding is not known as a common knowledge, the Cleveland Shiva Vishnu temple is very happy to share it.