# Binary Dihedral Group D₂*
#
# The quotient of the 3-sphere by the binary dihedral group D₂*
# (of order 8) gives a prism space based on a cube.
# In other words, the quotient space is a cube with opposite face pairs
# glued with left-handed π/2 rotations.
# This space is also known as the quaternionic manifold, because
# it’s the quotient of the group of unit-length quaternions (the 3-sphere)
# by the 8-element subgroup {±1, ±i, ±j, ±k} .
0 -1 0 0
1 0 0 0
0 0 0 1
0 0 -1 0
0 0 -1 0
0 0 0 -1
1 0 0 0
0 1 0 0