STATISTICS OF BASIC LAYPUTS IN THE STANDARD GEOMETRIC CHESS

    Please note that here we only display the basic layouts and the calculation of points must depend on which side making the last move to create and correlate the number of pieces involved in the layout (according to the rules of the game). There is no mention of polymorphic layout here.

  1. Straight line layout using the Axis piece (H.01).

* 1 Axis piece + 2 Point pieces

* 1 Axis piece + 3 Point pieces

* 1 Axis piece + 4 Point pieces

* 2 Axis pieces + 1 Point pieces

* 2 Axis pieces + 2 Point pieces

* 2 Axis pieces + 3 Point pieces

* 2 Axis pieces + 4 Point pieces

 (Axis piece position may be at the beginning, the end or in the middle of the segment, the Point pieces may be swapped. Straight lines may lie on the vertical axis or horizontal axis of the chessboard). 

Figure 01

   2. Straight line with equal distance using Cross piece (F.02)

* 1 Cross piece + 2 Point pieces

* 1 Cross piece + 3 Point pieces

* 1 Cross piece + 4 Point pieces

* 2 Cross pieces + 1 Point pieces

* 2 Cross pieces + 2 Point pieces

* 2 Cross pieces + 3 Point pieces

* 2 Cross pieces + 4 Point pieces

  (Cross piece position may be at the beginning, the end or in the middle of the segment, the Point pieces may be swapped. Straight lines may lie on the located on a diagonal of the chessboard ).

Figure 02

   3. Triangular layout with three chess pieces (F 03 & F 04)

 * 1 Triangular piece + 2 Point pieces

   In this case, the position of Triangular piece and Point pieces can be exchanged freely.

 * 1 Square piece + 1 Cross piece + 1 Point piece

 In this case, the positions of the Cross Pieces and Point Pieces can be swapped for each other, while the Square Piace must be at the top of the triangle. The hypotenuse of the triangle must be on the diagonal of the chessboard.

  * 1 Square Piece + 1 Axis Piece + 1 Point Pieces

  In this case, the position of the Axis Pieces and the Point Pieces can be swapped and the Square Piece must be at the top of the triangle. The hypotenuse of the triangle must lie on a vertical axis or horizontal axis of the board. 

Figure 03

   * 1 Acute piece + 1 Cross piece + 1 Point piece

   In this case, the Axis piece must be positioned at one of two acute corner tops of the triangle, while the Axis piece and the Point Piece may lie arbitrarily at the other two peaks. The hypotenuse of the triangle must lie on a vertical axis or horizontal axis of the board. 

  * 1 Acute piece+ 1 Axis piece + 1 Point Piece

   In this case, the Acute piece must be positioned at one of two acute corner tops of the triangle, while the Axis piece and the Dot Piece may lie arbitrarily at the other two peaks. The hypotenuse of the triangle must be on the diagonal of the chessboard.

  * 2 Cross pieces + 1 Axis piece

   In this case, the Axis piece must be positioned at one of two acute corner tops of the triangle, while other Cross pieces may lie arbitrarily at the other two peaks. The hypotenuse of the triangle must lie on a vertical axis or horizontal axis of the board. 

 * 2 Axis piece + 1 cross piece

   In this case, the Cross piece must be positioned at one of two acute corner tops of the triangle, while other Axis pieces may lie arbitrarily at the other two peaks. The hypotenuse of the triangle must be on the diagonal of the chessboard.

Figure 04

   4. Square layout with 4 chess pieces (F 05 & F 06)

  * 1 Quadrilateral piece+ 3 Point pieces

  In this case, the positions of the chess pieces can be arbitrarily swapped, the edges of the square can be located on the longitudinal axis and the horizontal axis or on the diagonal axis of the chessboard.

  * 1 Square piece + 2 Axis pieces + 1 Point pieces

  In this case, the edges of the square can only lie on the vertical and horizontal axes of the chessboard and the chess pieces can be swapped for each other.

Figure 05

  * 1 Square piece + 2 Cross pieces + 1 Point piece

  In this case, the edges of the square can only lie on the diagonal of the board, while the chess pieces can be swapped for each other.

  * 2 Square pieces + 2 Point pieces

  In this case, two Square pieces  must be placed symmetrically at two vertices of the square. The edges of the square can be located on the longitudinal axis and horizontal axis or on the diagonal of the chessboard

Figure 06

   5. Round layout with 4  or 5 chess pieces (F 07)

   * 1 Round piece + 3 Point pieces

   * 1 Round piece + 4 Point pieces

   In the case of round layout, the position of Round piece is always at the center of the circle, the Point pieces can be swapped for each other, the radius of the center with the points can be located on the vertical axis & horizontal axis or on the diagonal of the chessboard.

Hình 07

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