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パ:菱形多面体の菱形と正多角形

  • いわいまさか
  • at 2008/11/08 10:11:12

菱形多面体は

菱形十二面体    A
菱形十二面体2種  B
菱形二十面体           B
菱形三十面体           B

構成する菱形は二つの対角線の長さであらわすと

A 1 : √2
B 1 : (1+√5)/2

参考ページ:http://www5d.biglobe.ne.jp/~MY55029/subD401.htm

/////

ここで「ちょ、待てよ」と。

これは、1辺の長さと対角線の長さだとすると、

正方形   1:√2
正五角形  1:(1+√5)/2

と同じだと気づいた!!!

/////

1辺の長さと対角線の長さは他の正多角形で

正三角形 1:1  (対角線はないが拡大解釈して)
正六角形   1:2  あるいは
正六角形 1:√3

/////

 対角線の長さ1:1の菱形は正方形。
 正方形は、「正菱形六面体?」にあたる立方体を構成するという。

 というお話。


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