■置換多面体の空間充填性(その149)

 (その140)で,アルゴリズムは正多面体でもあてはまることをみたが,6次元でも確かめておきたい.

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[1]{3,3,3,3,3}(1,0,0,0,0,0)

  f5=(0/1+0/2+0/3+0/4+0/5+6/6)f0=(7)+(21)+(35)+(35)+(21)+7=7

  1は{3,3,3,3}(0,0,0,0,0)の頂点数=1

  2は{3,3,3}(0,0,0,0)×{}(1)の頂点数=1×2=2

  3は{3,3}(0,0,0)×{3}(1,0)の頂点数=1×3=3

  4は{3}(0,0)×{3,3}(1,0,0)の頂点数=1×4=4

  5は{}(0)×{3,3,3}(1,0,0,0)の頂点数=1×5=5

  6は{3,3,3,3}(1,0,0,0,0)の頂点数=6

[2]{3,3,3,4}(1,0,0,0,0,0)

  f5=(0/1+0/2+0/3+0/4+0/5+32/6)f0=(12)+(60)+(160)+(240)+(192)+64=64

  1は{3,3,3,4}(0,0,0,0,0)の頂点数=1

  2は{3,3,4}(0,0,0,0)×{}(1)の頂点数=1×2=2

  3は{3,4}(0,0,0)×{3}(1,0)の頂点数=1×3=3

  4は{4}(0,0)×{3,3}(1,0,0)の頂点数=1×4=4

  5は{}(0)×{3,3,3}(1,0,0,0)の頂点数=1×5=5

  5は{3,3,3,3}(1,0,0,0,0)の頂点数=6

[3]{3,3,3,3,4}(0,0,0,0,0,1)

  f5=(6/32+0/16+0/8+0/4+0/2+0/1)f0=12+(60)+(160)+(240)+(192)+(64)=12

  32は{3,3,3,4}(0,0,0,0,1)の頂点数=32

  16は{3,3,4}(0,0,0,1)×{}(0)の頂点数=16×1=16

  8は{3,4}(0,0,1)×{3}(0,0)の頂点数=8×1=8

  4は{4}(0,1)×{3,3}(0,0,0)の頂点数=4×1=4

  2は{}(1)×{3,3}(0,0,0)の頂点数=2×1=2

  1は{3,3,3,3}(0,0,0,0,0)の頂点数=1

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