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Polyhedra WorldMenuUpdated: 2009-4-11 14:13 UTC+8:00  Creator: Administrator [1]

 说明
Show/Hide ContentMenuCreated: 2009-4-9 16:02 UTC+8:00  Creator: Administrator [1]

特别说明
本站原来位于域名 www.viviasoft.com 下, 由于域名被他人抢注, 现移至域名 www.supertree.org 下.

源起
在中学时期, 作者曾对多面体着迷,用手工方式计算过一些多面体,用纸皮做过十多个多面体模型。后来从事软件设计工作,一直想利用计算机完成以前的一些设想。
再后来进入互联网,才知道早在几千年前多面体已被研究得相当完善,如在google上使用关键词 "Platonic polyhedra" 或 "Archimedean polyhedra",可查找到几千个关于多面体的英文网站。但中文网站几乎没有。

网站简介
网站使用了一个Flash多面体数据解析器,演示传统多面体及其扩展的结构;展示了对一个多面体子集的遍历程序及其运算结果;以及其它有关的内容。目前内容还较少,欢迎对此感兴趣的朋友能提供更多的资料以充实这个网站。

下一步工作
有一些问题作者还没有找到答案。由正多边形组合而成的多面体是否可穷举?它们是怎样的?例如给定一个k(k>3),由3,4,...,k边形组成的多面体是否可以穷举并一一列出。
实际上这个问题已被Johnson于1966年证明,除Platonic polyhedra和Archimedean polyhedra外,还有92种这样的多面体.但是作者认为,再次从计算机算法的角度考虑这个问题还是有一定的意义的.
如果时间允许, 下一步的工作,是完成对所有由正多边形组成的多面体遍历。如果有朋友对这个问题感兴趣,或有特别的见解,可与作者联系相互交流。

 Polyhedra
Show/Hide ContentMenuUpdated: 2009-4-9 13:20 UTC+8:00  Creator: Administrator [1]
Show/Hide ContentMenuUpdated: 2004-10-18 5:44 UTC+8:00
The Platonic Solids consist of surfaces of a single kind of regular polygon, with identical vertices.
Show/Hide ContentMenuUpdated: 2003-7-21 22:18 UTC+8:00
The Archimedean Solids, consist of surfaces of more than a single kind of regular polygon, with identical vertices and identical arrangements of polygons around each polygon.
Show/Hide ContentMenuUpdated: 2003-9-15 2:59 UTC+8:00
The vertexes of these polyhedra are constituted or surrounded by same combination of regular polygons, but the permutation of the polygons are more than one kind.
Show/Hide ContentMenuUpdated: 2009-4-9 11:17 UTC+8:00
All the convex polyhedra with regular polygon faces.
 Dual Polyhedron
Show/Hide ContentMenuUpdated: 2009-4-9 11:35 UTC+8:00  Creator: Administrator [1]
By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations.
ref: http://mathworld.wolfram.com/DualPolyhedron.html
 Dual Platonic Polyhedra
Show/Hide ContentMenuUpdated: 2004-1-9 22:05 UTC+8:00  Creator: Administrator [1]
tetrahedron ---> tetrahedron
cube ---> octahedron
octahedron ---> cube
dodecahedron ---> icosahedron
icosahedron ---> dodecahedron
Show/Hide ContentMenuUpdated: 2009-4-9 11:20 UTC+8:00
 Other Polyhedra
Show/Hide ContentMenuUpdated: 2009-4-9 13:20 UTC+8:00  Creator: Administrator [1]
Show/Hide ContentMenuUpdated: 2004-1-22 7:14 UTC+8:00
Show/Hide ContentMenuUpdated: 2004-3-8 2:21 UTC+8:00
There are only 7 convex hexhedron.
Show/Hide ContentMenuUpdated: 2009-6-25 0:39 UTC+8:00
 Simple 3D Object
Show/Hide ContentMenuUpdated: 2003-7-29 5:59 UTC+8:00  Creator: Administrator [1]
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Show/Hide ContentMenuUpdated: 2009-4-9 11:36 UTC+8:00
The data in this class are provided by Solventsky.
Show/Hide ContentMenuUpdated: 2009-4-9 11:37 UTC+8:00
The data in this class are mainly provided by Solventsky.
Show/Hide ContentMenuUpdated: 2009-4-9 11:37 UTC+8:00
The data in this class are mainly provided by Solventsky.
Show/Hide ContentMenuUpdated: 2009-4-11 14:45 UTC+8:00
Show/Hide ContentMenuUpdated: 2010-5-14 7:58 UTC+8:00
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