Avicenna numbers that we define in this paper, are a class of figurate numbers, including icosahedral, octahedral, tetrahedral, dodecahedral, rhombicosidodecahedral numbers and cubes, play a key role in mathematics, physics and various scientific fields. These numbers describe point arrangements in symmetrical 3D shapes and are essential in number theory, combinatorics, and geometric symmetry. They have practical applications in fields like chemistry, biology, materials science, virology, and network theory, helping model atomic arrangements, molecular structures, crystal lattices, viral capsids, and optimal networks. In this paper, we give some mathematical properties of Avicenna numbers that includes platonic and Archimedean numbers. Avicenna numbers satisfy fourth-order linear recurrence relations. Also, we mention their applications and relations to mathematics, physics and other sciences.