## 3 Results and Discussion
### Torsion Properties  
One end of the structure was fully constrained with six degrees of freedom, while angular displacement was applied to the other end. To obtain the torsional load, the reaction torque of the end face was fixed once the torsion angle was determined. We employed a similar testing approach to the compression test in our torsion experiment. The specimen was placed into the torsion instrument and loaded at a constant angular displacement rate of 1 degree per second until failure occurred. To minimize the impact of friction on the experimental results, we utilized the same friction-free boundary conditions as we did with the compression test and placed polyethylene sheets between the sample surface and the loading platen. Figure 6a demonstrates the torque-torque angle curve of the three samples and theoretical model of BS-7, which indicates that the torque increases with the increase in torque angle. When the torque angle reaches 22-23\({}^{\circ}\), the torque of the BS-7 structure reaches its maximum, and then drops sharply. The experimental sample and theoretical calculation exhibit the same trend when the torsional angle is \(\leq\)20\({}^{\circ}\), and the torque values are very close, which indicates that they hold a very small error. Thus, the theoretical model effectively predicts the torque values of actual BSs. Figure 6b illustrates the torque-torque angle characteristic curve of different BSs. The torque of all BSs increases with the increase in the torque angle. Notably, compared with other BSs, the torque of BS-2 is significantly lower than that of other BSs, and it is also the first to cause damage. This indicates that the internal support structure of BS-2 reduces the torsional strength of thin tubes. Moreover, the torques of BS-3 and BS-5 of a single-layer structure are lower than those of BS-4, BS-6, and BS-7 of a double-layer structure. Figure 6c clearly demonstrates the torsional strength of different BSs. BS-2 has the lowest torsional strength, only 63.71 N \(\cdot\) m, and BS-4 has the highest torsional strength, 126.64 N \(\cdot\) m. The torsional strength of BS-3 and BS-5 is close to that of BS-1, and slightly better than that of BS-1. Compared with BS-1, their torsional strength is increased by 0.5% and 2.2%, respectively. This indicates that adding a polygonal structure inside the thin tube can improve its torsional strength. Figure 5: Quasi-static compression deformation mode of BS-7. Notably, the torsional strength of BS-4, BS-6, and BS-7 is higher than that of BS-3 and BS-5, and their values are similar. The internal structure of BS-3 is a single quadrilateral, while that of BS-4 makes up two quadrilaterals. The torsional strength of BS-3 is 18% lower than that of BS-4. The internal structure of BS-5 is a single hexagon, while the internal structure of BS-6 includes two hexagons. The torsional strength of BS-6 is 12.1% higher than that of BS-5, and its torsional performance is better than that of BS-5. Therefore, increasing the number of polygonal structures inside the thin tube effectively improves the torsional performance. More importantly, BS-4 has the highest torsional strength, which is 3.4% and 2.1% higher than BS-6 and BS-7, respectively. BS-6 uses two adjacent hexagons to increase torsional strength. Although hexagons are more regular and symmetrical than quadrilaterals, each side of a hexagon is longer, and the angles of the hexagon are smaller, which may lead to excessive stress concentration and affect the torsional strength of the material. For BS-7, its internal structure is composed of a quadrilateral and an adjacent hexagon. Although this design can improve the stability of the tube, the two shapes are quite different, which may cause uneven stress distribution during torsion and reduce the torsional strength of the tube.