Uncharged pi meson

Description of tetrahedrons

This group is similar in shape to the charge pi meson but centered on six tetrahedrons instead of one. The 72 matrices used to form this group are as follows.

I





























(1)














(2)









(3)

(4)


(21)









(41)




(12)




(42)




(43)

(14)
(24)
(34)
(121)




(321)

(421)


(141)

(241)

(341)
(312)

(412)


(142)

(242)

(342)
(343)




(4121)




(4321)

(1421)
(2421)
(3421)
(2141)
(3141)
(1241)
(3241)

(4312)

(1412)
(2412)
(3412)
(2142)
(3142)
(1242)
(3242)

(1343)
(2343)



(14121)

(24121)

(34121)
(34321)




(12141)
(43141)

(43241)

(34312)




(12142)
(43142)

(43242)

(41343)
(42343)



(214121)
(314121)
(124121)
(324121)

(134321)
(234321)








(134312)
(234312)













(1214121)
(4314121)

(4324121)

(4134321)
(4234321)








(4134312)
(4234312)













The sum of all the matrices used to generate this shape is

0
0
0
0
0
0
0
0
0
0
189
189
207
261
0
108
108
117
162
0
-225
-225
-252
-351
72

The sum of columns is (0 0 846 495 1341)
The sum of products is 846*495 = 418770
The volume ratio is sqrt(418770/6) = 264.187
Th mass ratio of an uncharged pi meson to an electron is 264.143

A projection of this shape onto a plane follows.