■置換多面体の空間充填性(その372)

 5次元の正単体と正軸体の場合を比較したい.

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[1]{3,3,3,3}(10000)

  {3,3,3}(0000)0個→(10000),1個

  {3,3}(000)×{}(1)0個→(10000),5個

  {3}(00)×{3}(10)0個→(10000),10個

  {}(0)×{3,3}(100)0個→(10000),10個

  {3,3,3}(1000)5個→(10000),5個

0,5

0,0,10

0,0,0,10

0,0,0,0,5

[1]{3,3,3,4}(10000)

  {3,3,4}(0000)0個→(10000)1個

  {3,4}(000)×{}(1)0個→(10000)8個

  {4}(00)×{3}(10)0個→(10000)24個

  {}(0)×{3,3}(100)0個→(10000)32個

  {3,3,3}(1000)16個→(10000)16個

0,8

0,0,24

0,0,0,32

0,0,0,0,0,16

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[2]{3,3,3,3}(01000)

  {3,3,3}(1000)2個→(14641),2個

  {3,3}(000)×{}(0)0個→(1000),1個

  {3}(00)×{3}(01)0個→(1000),4個

  {}(0)×{3,3}(010)0個→(1000),6個

  {3,3,3}(0100)4個→(1000),4個

2,−1

8,0

12,0,4

8,0,0,6

2,0,0,0,4

[2]{3,3,3,4}(01000)

  {3,3,4}(1000)2個→(1,6,12,8,1)2個

  {34}(000)×{}(0)0個→(1000)1個

  {3}(00)×{3}(01)0個→(1000)6個

  {}(0)×{3}(010)0個→(1000)12個

  {3,3,3}(0100)8個→(10000)8個

2,−1

12,0

24,0,6

16,0,0,12

2,0,0,0,8

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[3]{3,3,3,3}(00100)

  {3,3,3}(0100)3個→(16951),3個

  {3,3}(100)×{}(0)0個→(13310),3個

  {3}(00)×{3}(00)0個→(1000),1個

  {}(0)×{3,3}(001)0個→(1000),3個

  {3,3,3}(0010)3個→(1000),3個

3,−3,1

18,−9,0

27,−9,0

15,−3,0,3

3,0,0,0,3

[3]{3,3,3,4}(00100)

  {3,3,4}(0100)3個→(1,8,12,6,1)3個

  {3,4}(100)×{}(0)0個→(14410)3個

  {4}(00)×{3}(00)0個→(1000)1個

  {}(0)×{3}(001)0個→(1000)4個

  {3,3,3}(0010)4個→(10000)4個

3,−3,1

24,−12,0

36,−12,0

18,−3,0,4

3,0,0,0,4

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[4]{3,3,3,3}(00010)

  {3,3,3}(0010)4個→(16951),4個

  {3,3}(010)×{}(0)0個→(14410),6個

  {3}(10)×{3}(00)0個→(12100),4個

  {}(0)×{3,3}(000)0個→(1000),1個

  {3,3,3}(0001)2個→(1000),2個

4,−6,4,−1

24,−24,8,0

36,−24,4,0

20,−6,0,0

4,0,0,0,2

[4]{3,3,3,4}(00010)

  {3,3,4}(0010)4個→(1,6,9,5,1)4個

  {3,4}(010)×{}(0)0個→(14410)6個

  {4}(10)×{3}(00)0個→(12100)4個

  {}(0)×{3}(000)0個→(1000)1個

  {3,3,3}(0001)2個→(10000)2個

4,−6,4,−1

24,−24,8,0

36,−24,4,0

20,−6,0,0

4,0,0,0,2

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[5]{3,3,3,3}(00001)

  {3,3,3}(0001)5個→(14641),5個

  {3,3}(001)×{}(0)0個→(13310),10個

  {3}(01)×{3}(00)0個→(12100),10個

  {}(1)×{3,3}(000)0個→(11000),5個

  {3,3,3}(0000)0個→(10000),1個

5,−10,10,−5,1

20,−30,20,−5,0

30,−30,10,0,0

20,−10,0,0,0

5,0,0,0,0

[5]{3,3,3,4}(00001)

  {3,3,4}(0001)5個→(1,4,6,4,1)5個

  {3,4}(001)×{}(0)0個→(13310)10個

  {4}(01)×{3}(00)0個→(12100)10個

  {}(1)×{3}(000)0個→(1100)5個

  {3,3,3}(0001)0個→(10000)1個

5,−10,10,−5,1

20,−30,20,−5,0

30,−30,10,0,0

20,−10,0,0,0

5,0,0,0,0

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[まとめ]この方針は順調に機能している.

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