By means of first-principles calculations, we studied in detail the structural, elastic, and electronic properties of the tetragonal CaBe 2 Ge 2 -type 5.2 K superconductor SrPt 2 As 2 in comparison with two hypothetical SrPt 2 As 2 polymorphs with ThCr 2 Si 2 -type structures, which differ in the atomic configurations of the [Pt 2 As 2 ] (or [As 2 Pt 2 ]) blocks. We found that CaBe 2 Ge 2 -type SrPt 2 As 2 is a unique system with near-Fermi bands of a complicated character and an "intermediate"-type Fermi surface, which consists of electronic pockets having a cylinderlike [two-dimensional (2D)] topology (typical of 122 FeAs phases) together with 3D-like electronic and hole pockets, which are characteristic of ThCr 2 Si 2 -like iron-free low-T c superconductors. Our analysis revealed that, as distinct from ThCr 2 Si 2 -like 122 phases, other features of CaBe 2 Ge 2 -like SrPt 2 As 2 are as follows: (1) There are essential differences in the contributions from [Pt 2 As 2 ] and [As 2 Pt 2 ] blocks to the near-Fermi region; conduction is anisotropic and occurs mainly in the [Pt 2 As 2 ] blocks. (2) A 3D system of strong covalent Pt-As bonds is formed (inside and between [Pt 2 As 2 ] and [As 2 Pt 2 ] blocks), which is responsible for enhanced stability of this polymorph.(3) There is essential charge anisotropy between adjacent [Pt 2 As 2 ] and [As 2 Pt 2 ] blocks. We also predict that CaBe 2 Ge 2 -like SrPt 2 As 2 is a mechanically stable and relatively soft material with high compressibility, which will behave in a ductile manner. In contrast, the ThCr 2 Si 2 -type SrPt 2 As 2 polymorphs, which contain only [Pt 2 As 2 ] or [As 2 Pt 2 ] blocks, are less stable, have Fermi surfaces of a multisheet three-dimensional type like the ThCr 2 Si 2 -like iron-free 122 phases, and therefore will be ductile materials with high elastic anisotropy. Based on our data for the three simplest SrPt 2 As 2 polymorphs we assume that there may exist a family of higher-order polytypes, which can be formed as a result of various stackings of the two main types of building blocks ([Pt 2 As 2 ] and [As 2 Pt 2 ]) in various combinations along the z axis. This may provide an interesting platform for further theoretical and experimental search for other superconducting materials.