與正十二面體相關的幾何構造

Geometric constructions associated with the regular dodecahedron

葉晉嘉(Chin-Chia Yeh)

指導教授 ： 全任重

國立清華大學/理學院/數學系/碩士(2007年)

摘要

正十二面體是柏拉圖多面體其中的一個，由於正十二面體每一個面都是正五邊形。因此，提供了相當多的發展性，此篇論文藉由動態幾何軟體Cabri3D探討了正十二面體的相關性質，以及利用正十二面體出發建構了與星狀多面體或Catalan多面體相關之多面體。

關鍵字

正十二面體 ； 幾何

並列摘要

The regular dodecahedron has 12 faces and 20 vertexes. Each faces of the regular dodecahedron is a regular pentagon. In short, the regular dodecahedron can be employed in many ways. There are several sections in this study. For the first section, it talked about the duality of regular dodecahedron. The second and third section described about the relationship between regular dodecahedron and other stuffs. The fourth section discussed about using the regular dodecahedron to construct the certain polyhedrons. And, those polyhedrons are related to stellated polyhedrons. The final section talked about using the regular dodecahedron to construct the certain polyhedrons. And, those polyhedrons are related to Catalan solids.
This paper presents the design of Polyhedron under Cabri3D, interactive dynamic software of geometry. It is divided into five sections. You can crystal clearly to discover the detail in the website:
http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/g943251/dynamic/index.htm
Here you can see the production of this study and application of 3D dynamic geometry.

參考文獻

References

[1] http://poncelet.math.nthu.edu.tw/

[2] http://whistleralley.com/polyhedra/dodecahedron.htm

[3] http://en.wikipedia.org/wiki/Dodecahedron

[4] http://mathworld.wolfram.com/