■等面単体の体積(その156)
4次元正単体(辺の長さ1)
(−1/2,−√3/6,−√6/12,−√10/20)
(+1/2,−√3/6,−√6/12,−√10/20)
(0,√3/3,−√6/12,−√10/20)
(0,0,√6/4,−√10/20)
(0,0,0,0,√10/5)
を平行移動させる
A(0,0,0,0,0)
B(1,0,0,0,a)
C(1/2,√3/2,0,0,2a)
D(1/2,√3/6,√6/3,0,3a)
E(1/2,√3/6,√6/3,√10/4,4a)
F(0,0,0,0,5a)
b^2=1+a^2
c^2=1+4a^2
d^2=1+9a^2
e^2=1+16a^2
5a=eとおくと,
25a^2=1+16a^2,a^2=1/9
b^2=10/9,c^2=13/9,d^2=2,e^2=25/9
5a=dとおくと,
25a^2=1+9a^2,a^2=1/16
b^2=17/16,c^2=20/16,d^2=25/16,e^2=2
5a=cとおくと,
25a^2=1+4a^2,a^2=1/21
b^2=22/21,c^2=25/21,d^2=30/21,e^2=37/21
5a=bとおくと,
25a^2=1+a^2,a^2=1/24
b^2=25/24,c^2=28/24,d^2=31/24,e^2=40/24
===================================