**7. Methods and results**

The stereoscopic system generates the following two types of objects studied in the discipline of stereometry:


There are two main techniques involved in generating a regular polygon in the stereoscopic system; the first is the traditional one that converts a 2D polygon into a 3D object. This is done by extruding a two-dimensional graphic into a three dimensional one. The extrusion technique creates a three-dimensional object from a two-dimensional that moves along a set trajectory. The trajectory can be a rotational or translational motion or a trajectory defined by an arbitrary curve. In the research on the generation of a quadrangular pyramid, a new boundary method is used, which is based on Cavalieri's Indivisible method and Newton's boundary method [11, 12]. The idea is as follows—the geometric figure must be divided into sections parallel to a given ruler. This approach can be applied to any regular polygon. Next, determine the relations of the parallel sections. In the case of four vertices, i.e., a square (regular polygon), the ratio of the segments is 1:1. Polygon vertices can grow without limit. Regular polygons generated in this way differ from traditional programming polygons because they do not need to be converted from a 2D to a 3D object by extruding. They are "mathematically more accurate" and more flexible than traditional ones. They have many advantages, the biggest one being that virtual reality devices can visualize them. At the same time, they can be exported to files with the extension .obj. It follows that the polygon is placed in the center of the coordinate axis and its vertices are calculated by the length of its side by the parameter **a**. To parametrically define a regular quadrangular pyramid, the values for each vertex of the three-dimensional space

#### **Figure 1.**

*Edge representation of the base of the pyramid.*

#### **Figure 2.**

*Limit representation of a pyramid.*

should be defined. The parameter "a" is the length of the side of the polygon that is the base of the pyramid. The parameter **h** is the height of the pyramid. When the value of vertex No. 5 is a number other than zero on the abscissa or ordinate, the final result will be a tilted pyramid. The system also enables the generation of a truncated pyramid. The methods for 3D geometric modeling and their schematic representation is done in two ways: edge and boundary. The edge representation (**Figure 1**) requires the following information:

The object's shape is represented by its edges (E1, E2,…).

1.Vertices metric information (A, B, C,…).

2.Partial topological information (X1, Y1, Z1,…).

The boundary representation of a regular quadrilateral pyramid presented in (**Figure 2**) requires:

1.List of all its walls (W1, W2,…)—W6 is the section of the pyramid
