■置換多面体の空間充填性(その110)

 空間充填2^n+2n胞体において,切頂点に集まるn−1次元面数は

  (tp+1,1)+2^n-1-fp

になりましたが,これは空間充填2^n+2n胞体に限らず,一般の正軸体系切頂型準正多胞体でも成り立つ式のはずである.

  fn-1=(x/a+y/b)f0

念のため,検してみたい.

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【1】n=3

{3,4}(010);f2=(2/4+2/3)f0=6+8=14

{3,4}(110);f2=(1/4+2/6)f0=6+8=14

{3,4}(011);f2=(2/8+1/3)f0=6+8=14

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【2】n=4

{3,3,4}(0100);f3=(2/6+4/6)f0=8+16=24

{3,3,4}(0010);f3=(3/12+2/4)f0=8+16=24

{3,3,4}(1100);f3=(1/6+4/12)f0=8+16=24

{3,3,4}(0110);f3=(2/24+2/12)f0=8+16=24

{3,3,4}(0011);f3=(3/24+1/4)f0=8+16=24

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【3】n=5

{3,3,3,4}(01000);f4=(2/8+8/10)f0=10+32=42

{3,3,3,4}(00100);f4=(3/24+4/10)f0=10+32=42

{3,3,3,4}(00010);f4=(4/32+2/5)f0=10+32=42

{3,3,3,4}(11000);f4=(1/8+8/20)f0=10+32=42

{3,3,3,4}(01100);f4=(2/48+4/30)f0=10+32=42

{3,3,3,4}(00110);f4=(3/96+2/20)f0=10+32=42

{3,3,3,4}(00011);f4=(4/64+1/5)f0=10+32=42

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【4】n=6

{3,3,3,3,4}(010000);f5=(2/10+16/15)f0=12+64=76

{3,3,3,3,4}(001000);f5=(3/40+8/20)f0=12+64=76

{3,3,3,3,4}(000100);f5=(4/80+4/15)f0=12+64=76

{3,3,3,3,4}(000010);f5=(5/80+2/6)f0=12+64=76

{3,3,3,3,4}(110000);f5=(1/10+16/30)f0=12+64=76

{3,3,3,3,4}(011000);f5=(2/80+8/60)f0=12+64=76

{3,3,3,3,4}(001100);f5=(3/240+4/60)f0=12+64=76

{3,3,3,3,4}(000110);f5=(4/320+2/30)f0=12+64=76

{3,3,3,3,4}(000011);f5=(5/160+1/6)f0=12+64=76

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