臺灣博碩士論文加值系統

利用3D動態幾何研究阿基米德與強森凸面體

An interesting geometrical convex solids are actually the 13 Archimedean solids and 92 Johnson solids. The Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the same way about each vertex with all sides the same length (Cromwell 1997, pp. 91-92). The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" Archimedean solids, and the two infinite families of prisms and antiprisms). There are 28 simple (i.e., cannot be dissected into two other regular-faced polyhedra by a plane) regular-faced polyhedra in addition to the prisms and antiprisms (Zalgaller 1969), and Johnson (1966) proposed and Zalgaller (1969) proved that there exist exactly 92 Johnson solids in all.
This paper presents the design of Archimedean and Johnson solids under Cabri 3D Geometry , interactive dynamic software of geometry. It is divided into twelve sections. You can see the detail clearly in the website:
http://140.114.32.3/d3/johnson-solids/
Here anyone can see my achievement easily and the application of 3D dynamic geometry.

Contents
Page

I. Abstract ．．．．．．．．．．．．．．．．．．．．．．．．． ．．．1
II. Preface．．．．．．．．．．．．．．．．．．．．．．．．．．．．．2
III. Section 1：Introduction to Archimedean Solid ．．．．．．．．．．．．4
IV. Section 2：Fundamental Archimedean Solids．．．．．．．．．．．．．5
V. Section 3：Johnson Solids．．．．．．．．．．．．．．．．．．．．．8
VI. Section 4：Prisms．．．．．．．．．．．．．．．．．．．．．．．．10
VII. Section 5：Rotunda．．．．．．．．．．．．．．．．．．．．．．．14
VIII. Section 6：Cupola．．．．．．．．．．．．．．．．．．．．．．．．17
IX. Section 7：Pyramids．．．．．．．．．．．．．．．．．．．．．．．25
X. Section 8：Dodecahedron．．．．．．．．．．．．．．．．．．．．．30
XI. Section 9：Cupola-Rotunda．．．．．．．．．．．．．．．．．．．．32
XII. Section 10：Icosahedron．．．．．．．．．．．．．．．．．．．．．34
XIII. Section 11：Truncated Solids．．．．．．．．．．．．．．．．．．．35
XIV. Section 12：Unable to construct solids ．．．．．．．．．．．．．． 38
XV . Reference ．．．．．．．．．．．．．．．．．．．．．．．．．． 41

http://sylvester.math.nthu.edu.tw/d2/gc-04/
http://mathworld.wolfram.com/topics/LiveGraphics3DApplets.html