■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
1
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
1
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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