Abstract
Toric variety is a branch of algebraic geometry where combinatorics and algebraic geometry substantiate each other. In this paper we will explore how to construct abstract toric variety that can be described purely by algebraic data without embedding into affine or projective spaces from concrete combinatorial data. Two method will be introduced. The first one uses a polytope and the second one a fan. We will present how to construct a fan associated with a polytope and prove that these two methods yield isomorphic toric varieties. Finally, Galois Correspondence appears when we consider everything we have done in duality.