1895年，由「Icosion Game」發展而來的圖論問題哈密頓迴路。
本論文將探討如何用Cabri 3D在正多面體上找到哈密頓迴路，並將其定義延伸到多面體的展開圖，進而探討展開圖上哈密頓迴路與其對偶多面體的關係。
1.我們將會用投影、貪婪法跟正多面體的對稱性來輔助我們尋找哈密頓迴路。
2.對偶多面體的點面對換性質將有助於我們尋找展開圖上哈密頓迴路。

The Icosian Game and the Hamiltonian cycle in graph theory was invented in the 1895s. We will use Cabri 3D to find Hamiltonian cycles on polyhedron, and expand to nets of polyhedron to find relation between Hamiltonian cycles and dual polyhedron.
1.We will use projection, greedy algorithm, and symmetry of polyhedron to find Hamiltonian cycles.
2.Vertices to face property in dual helps us to Hamiltonian cycles on nets.

List of Figures vi
1 Introduction 1
2 Construction of Hamiltonian Cycles 2
2.1 Method 1: Projection 2
2.2 Method 2: Greedy Algorithm 4
3 Net of Polyhedron 6
3.1 Nets of Cube 7
3.2 Nets on Dual Pair Cube-Octahedron 8
3.3 Nets on Dual Pair Dodecahedron-Icosahedron 12
4 References 15

[1] Martin Gardner, Hexaflexagons and other mathematical diversions, First Edition, pp. 55-62
[2] Net of Polyhedron, Wikipedia,
https://en.wikipedia.org/wiki/Net_(polyhedron)
[3] The 11 cubic nets.svg, Wikipedia, https://upload.wikimedia.org/wikipedia/commons/c/cd/The_11_cubic_nets.svg
[4] Number of Nets, Wolfram MathWorld,
http://mathworld.wolfram.com/Net.html
[5] Hamilton Cycle, Wolfram MathWorld,
http://mathworld.wolfram.com/HamiltonianCycle.html