■高次元タイルの二面角(その8)

 空間充填2(2^n−1)胞体の二胞角は

  cosδ=−{(j+1)/(k+1)・(n−k)/(n−j)}^1/2

で与えられる.

 n=6の場合

  cosδ01=−{1/2・5/6}^1/2=−√(5/12)

  cosδ02=−{1/3・4/6}^1/2=−√(2/9)

  cosδ03=−{1/4・3/6}^1/2=−√(1/8)

  cosδ04=−{1/5・2/6}^1/2=−√(1/15)

  cosδ05=−{1/6・1/6}^1/2=−1/6

  cosδ12=−{2/3・4/5}^1/2=−√(8/15)

  cosδ13=−{2/4・3/5}^1/2=−√(3/10)

  cosδ14=−{2/5・2/5}^1/2=−2/5

  cosδ15=−{2/6・1/5}^1/2=−√(1/15)

  cosδ23=−{3/4・3/4}^1/2=−3/4

  cosδ24=−{3/5・2/4}^1/2=−√(3/10)

  cosδ25=−{3/6・1/4}^1/2=−√(1/8)

  cosδ34=−{4/5・2/3}^1/2=−√(8/15)

  cosδ35=−{4/6・1/3}^1/2=−√(2/9)

  cosδ45=−{5/6・1/2}^1/2=−√(5/12)

===================================

  cosδ01=−√(5/12),δ1=130.203

  cosδ02=−√(2/9),δ2=118.125

  cosδ03=−√(1/8),δ3=110.705

  cosδ04=−√(1/15),δ4=104.963

  cosδ05=−1/6,δ5=99.594

  cosδ12=−√(8/15),δ6=136.911

  cosδ13=−√(3/10),δ7=123.211

  cosδ14=−−2/5,δ8=113.578

  cosδ15=−√(1/15),δ4=104.963

  cosδ23=−3/4,δ9=138.59

  cosδ24=−√(3/10),δ7=123.211

  cosδ25=−√(1/8),δ3=110.705

  cosδ34=−√(8/15),δ6=136.911

  cosδ35=−√(2/9),δ2=118.123

  cosδ45=−√(5/12),δ1=130.203

  2δ1+δ5=360°

  2δ3+δ9=360°

  2δ7+δ8=360°

  δ2+δ4+δ6=360°

 念のため,解析的にも検してみると,

  arccos(√2/9)+arccos(√1/15)

=arccos(√2/9√1/15−√7/9・√14/15)

=arccos(−√8/15)=δ6

===================================