### Geometry of the Binary Tetrahedral Group in SU(2)

## Vertices

The elements of order six are +/-a, +/-a^2,
+/-b, +/-b^2,
+/-c, +/-c^2, +/-d, +/-d^2, where

a = (1/2) ( 1- i- j- k),

b = (1/2) ( 1- i+ j+ k),

c = (1/2) ( 1+ i- j+ k),

d = (1/2) ( 1+ i+ j- k).

The elements of order four are
+/- i, +/- j, +/- k;

1 and - 1 complete the list of 24 elements.

(See The Quaternionic Representation of the Binary
Tetrahedral Group for the derivation of these elements from
symmetries of the tetrahedron.)

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