#one point from each unitary (positive semidefinite) facet
#in standard coordinates
(7/8,1/4,1/4)
(0,0,0)
(3/4,1/2,1/4)
(1,1/4,1/4)
(3/4,1/2,1/2)
(3/4,1/4,0)
(1,3/4,0)
(1,3/4,1/4)
(3/4,3/4,1/4)
(3/4,1/4,1/4)
(1,0,0)
(1,1,0)
(1/2,1/2,1/2)
(3,2,1)
(2,1,0)