在我們的論文中，我們所有的動態幾何實驗的背景環境都是利用Cabri 3D這個軟體。
在我們的論文中，我們研究：
1.有關截角化立方體以及三角化多面體的對稱模式。
2. 有關截角化立方體以及三角化多面體的第一種動態模擬模式。
3. 有關截角化立方體以及三角化多面體的第二種動態模擬模式。
4.三種用此方法做推廣的對偶多面體
(1) 截半立方體以及菱形十二面體
(2) 截半二十面體以及菱形三十面體
(3) 四面體以及四面體

All dynamic geometric experiments carried out for this work are performed in the interactive geometry environment created by the software Cabri 3D.
In this paper, we study
1.Symmetric Patterns associated with the pair Truncated Cube-Triakis Octahedron.
2.First Distorted Patterns associated with the pair Truncated Cube -Triakis Octahedron. This pattern has a fixed symmetrc axis of rotation.
3.Second Distorted Patterns of the pair Truncated Cube-Triakis Octahedron. This pattern has two invariant incircles of the faces.
4. extension of 3 to the pairs
(a) Cuboctahedron-Rhombic Dodecahedron
(b) Icosidodecahedron-Rhombic Triacontahedron
(c) Tetrahedron-Tetrahedron

1. John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, A K Peters CRC Press (2008).
2. R. A. Johnson, Advanced Euclidean Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle (1960).
3. H. A. Miers, An Enquiry into the Variation of Angles Observed in Crystals, Especially of PotassiumAlum and Ammonium-Alum., Proceedings of the Royal Society of London, Vol. 71 (1902 - 1903), pp. 439-441.
4. https://en.wikipedia.org/wiki/Dual_polyhedron
5. https://mathworld.wolfram.com/TruncatedCube.html
6. https://mathworld.wolfram.com/SmallTriakisOctahedron.html
7. https://mathworld.wolfram.com/CatalanSolid.html