The Lingam is an abstract representation of the abstract concept of Shiva. As such, it has no prescribed form: the shape of this idol depends upon the understanding of Shiva to be conveyed, and the artistry by which the abstract artist conveys that understanding. The dual nature of Shiva requires it be presented simultaneously with another abstract representation of Shakti - the Yoni. Because dualism is best understood in terms of sexuality (male and female, both male and female, and neither male nor female), the Lingam is typically made in the form of a penis, or some other masculine shape of some kind. And the Yoni is typically made in the form of a uterus, or vagina, or some other feminine shape of some kind.
Depending on the concept which is to be conveyed, the Lingam and Yoni may be placed in union (the union of both male and female is typically represented by using the symbolic means of coupling), or individually (the co-arising individuality of male and female is represented so that male and female are understood to have meaning only in context of each other: what is "female" without "male," or "black" without "white?"), or separately (the nature of what is neither male nor female is understood only by the context of what is male and female through a difficult representation of the primordial nature of both male and female).
Abstract art is difficult, and relies on the introspection of symbology. What does "masculine" or "feminine" mean to you? Are "you" masculine or feminine? What is both masculine and feminine? What is neither masculine or feminine? The act of making the Lingam and Yoni permit an understanding of the illusionary nature of form, and the necessary logical fallacy of dualism in understanding quaternary logic. It permits right-understanding: it is inappropriate to describe something as male or female, except in the cultural and societal context of dualism: these concepts do not exist all on their own.
What is masculine to you may be different to someone else, or may have changed with time. Several hundred years ago, the very masculine American President George Washington wore high heels, tights and long hair - these are now feminine forms. Does this make George Washington less masculine? Or women today less feminine? Pants were frequently understood to be a symbol of masculinity. But these, too, change with time. Style is always changing - as is our understanding of what it is to be a man, or a woman.
Is a man one who loves what is woman? Or what is man? Is a man defined by what he is not? Or by what he is? How do you define yourself? How does this definition limit your being?
If we travel but a little, the horizon shifts - we can never reach the end of the sky. Even should we venture to the moon, or beyond - the sky is limitless.
In meditating on the Lingam, some remember also the story of the pillar of fire. One day, Brahma and Vishnu were arguing on the banks of the Kashi about which one of them was elder. Shiva manifested a pillar of light which extended across every space and time, and challenged each brother to find the limits of it before the other. Space and time have only the limits we define; these are abstract concepts of our imagination. Consequently, neither brother could succeed - even though one traveled in one direction and the other in the opposite, both found each other at the end of their searching. The Yoni is the origin of this light, the uterus by which form is birthed; that which transcends form, the non-duality which birthed duality. Is a mother one or two beings? The truth of the matter is that these terms do not apply, and cannot reveal the answer, for they are abstractions of form.
Our shrine has a Lingam and Yoni. Have fun adding one to yours.