■n次元平行多面体数(その96)

 (その93)において,n=4の回転行列は

[1,1/2,0,−1/2]

[0,1/2,1/√2,1/2]

[1,−1/2,0,1/2]

[0,1/2,−1/√2,1/2]

となるが,s=1/√2,t=1/2とおくと

[1,t,0,−t]

[0,t,s,t]

[1,−t,0,t]

[0,t,−s,t]

 (x,y,z)空間への投影を考えると

[1,0,0,0][1,t,0,−t]=[1,t,0,−t]

[0,1,0,0][0,t,s,t]  [0,t,s,t]

[0,0,1,0][1,−t,0,t] [1,−t,0,t]

[0,t,−s,t]

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