Page 150 - JCAU-6-2

Journal of Chinese
Architecture and Urbanism RuiXue Multi-Hall in reciprocal structures

Figure 8. Reciprocal geometry library. Source: Drawing by Yingzi Hu, editing by Yueyang Wang

It is worth emphasizing that certain regular polygon 4.4. Shell mapping of reciprocal geometry
grids, such as A-60, B-45, and C-30, may, when rotated at We explore three methods for applying the reciprocal
specific angles, form geometric patterns that do not exhibit
reciprocal relationships due to their inherent geometric geometric library to generate structural systems for
characteristics. Furthermore, when the rotation angle α desired shell surfaces. The first method begins with simpler
for all grid types is set to 90°, it results in the formation of a geometric surface shapes. The three-dimensional curved
stable coupled pattern that is the reverse of the initial grid. surface is directly subdivided into a basic grid composed of
However, this pattern also lacks a reciprocal relationship. equilateral triangles, squares, and hexagons. Subsequently,
In addition, we observe that A and C grids interact with line segments are rotated and extended around the
each other as the angle changes, leading to the creation of midpoint in three-dimensional space to complete the
reciprocal grids with consistent geometric features. transformation of the reciprocal grid in space (Figure 9).

Volume 6 Issue 2 (2024) 8 https://doi.org/10.36922/jcau.1635