I was inspired to create this video by the Penrose Tile and fifth-order symmetry =)
    
        int vertexes = 5; // Number of vertices
        PointF center = new PointF(300.0f, 300.0f); // Coordinates of the center of the circle
        float radius = 100; // Radius
        float angle = (float)Math.PI * 2 / 5;//Angle

    private void draw_polygon(float _center_X, float _center_Y, float k_x, float k_y, Pen silverPen4, float radius,  double angle_k)
        {
            using (var g = Graphics.FromImage(bmp))
            {
                PointF[] p = new PointF[vertexes];
                PointF center = new PointF(_center_X + radius * k_x, _center_Y + radius * k_y); // Coordinates of the center of the circle
                for (int i = 0; i < vertexes; i++)
                {
                    p[i] = new PointF(center.X + (float)Math.Sin(i * angle + angle_k) * radius, center.Y + (float)Math.Cos(i * angle + angle_k) * radius);
                }
                for (int i = 0; i < vertexes; i++)
                {
                    g.DrawPolygon(silverPen4, p);
                }
            }
        }
    in accordance with the dependent coordinates of the center
    in the proportions of magnification by means of coefficients
    Here is a straight and inverted pentagon:
    
 
        private void draw_polygons(PointF _center, Pen silverPen4, float radius) 
        {
            float a1 = 2 * (float)Math.Cos(Math.PI / 5);
            float a2 = a1 * (float)Math.Cos(Math.PI / 10);
            float a3 = a1 * (float)Math.Cos(4 * Math.PI / 5 - Math.PI / 2);
            float a4 = a1 * (float)Math.Sin(4 * Math.PI / 5 - Math.PI / 2);
            draw_polygon(_center.X, _center.Y,  0.0f, 0.0f, silverPen4, radius,  -Math.PI / 5);
            draw_polygon(_center.X, _center.Y,  a3, -a4, silverPen4, radius, 0.0);
            draw_polygon(_center.X, _center.Y,  -a3, -a4, silverPen4, radius,  0.0);
            draw_polygon(_center.X, _center.Y,  -a2, 0.5f, silverPen4, radius,  0.0);
            draw_polygon(_center.X, _center.Y,  a2, 0.5f, silverPen4, radius,  0.0);
            draw_polygon(_center.X, _center.Y,  0.0f, a1, silverPen4, radius, 0.0);
        }
        private void draw_polygons_i(PointF _center, Pen silverPen4, float radius)
        {
            float a1 = 2 * (float)Math.Cos(Math.PI / 5);
            float a2 = a1 * (float)Math.Cos(Math.PI / 10);
            float a3 = a1 * (float)Math.Cos(4 * Math.PI / 5 - Math.PI / 2);
            float a4 = a1 * (float)Math.Sin(4 * Math.PI / 5 - Math.PI / 2);
            draw_polygon(_center.X, _center.Y,  0.0f, 0.0f, silverPen4, radius,  0.0);
            draw_polygon(_center.X, _center.Y,  0.0f, -a1, silverPen4, radius,  -Math.PI / 5);
            draw_polygon(_center.X, _center.Y,  a2, -0.5f, silverPen4, radius,  -Math.PI / 5);
            draw_polygon(_center.X, _center.Y,  -a2, -0.5f, silverPen4, radius, -Math.PI / 5);
            draw_polygon(_center.X, _center.Y,  a3, a4, silverPen4, radius,  -Math.PI / 5);
            draw_polygon(_center.X, _center.Y,  -a3, a4, silverPen4, radius,  -Math.PI / 5);
        }
    Continuation of further calculation of new center coordinates with new coefficients
    and the compilation of even larger pentagons: 
    an example of new coefficients:
    
           float a01 = radius * (2 * a1 + 1) * (float)Math.Cos(Math.PI / 10);
            float a02 = radius * (2 * a1 + 1) * (float)Math.Sin(Math.PI / 10);
            float a03 = radius * (2 * a1 + 1) * (float)Math.Sin(Math.PI / 5);
            float a04 = radius * (2 * a1 + 1) * (float)Math.Cos(Math.PI / 5);
            float a05 = 0.0f;
            float a06 = radius * (2 * a1 + 1);
    You can continue by calculating the coefficients according to the Fibonacci sequence 
    or in a similar way:
    
 int s = 0; int n = 1; int p = 1;
            for (int i = 0; i < 4; i++)
            {
                s = n + p;
                float a_1_ = radius * (s * a1 + p) * (float)Math.Cos(Math.PI / 5);
                float a_2_ = radius * (s * a1 + p) * (float)Math.Sin(Math.PI / 5);
                float a_5_ = radius * (s * a1 + p);
                float a_3_ = radius * (s * a1 + p) * (float)Math.Cos(Math.PI / 10);
                float a_4_ = radius * (s * a1 + p) * (float)Math.Sin(Math.PI / 10);
                float a_6_ = 0.0f;
            
                n = p;
                p = s;
            }
    By changing the coordinate coefficients of the centers 
    and the radiuses of the pentagons over time, 
    i got this video (above)