Now we write the reflections in terms of this new basis. 1 Reflection through < 1 , 0 , 0 ,> is conjugate to -1 1+ 1x 0- 1x 0 1 0 0 0 1 Reduces mod 2 to 1 1 0 0 1 0 0 0 1 2 Reflection through < 0 , 1 , 1 ,> is conjugate to 1 1 0+ 1x 0 1 0 0 1+ 1x -1 Reduces mod 2 to 1 1 0 0 1 0 0 1 1 3 Reflection through < 0 , -1 , 1 ,> is conjugate to 1 -2- 1x 0 0 -1 0 0 -1- 1x 1 Reduces mod 2 to 1 0 0 0 1 0 0 1 1 4 Reflection through < 1 , 1 , -1- 1x ,> is conjugate to 0- 1x -1+ 1x 0 -1- 1x 0+ 1x 0 0- 1x -2 1 Reduces mod 2 to 0 1 0 1 0 0 0 0 1 5 Reflection through < -1 , 1 , -1- 1x ,> is conjugate to 1+ 1x 0 -2- 1x 1+ 1x 1 -2 0+ 1x 0 -1- 1x Reduces mod 2 to 1 0 0 1 1 0 0 0 1 6 Reflection through < 1 , 1 , 1+ 1x ,> is conjugate to 2+ 1x 1- 1x -1+ 1x 1 0- 1x 1+ 1x 0+ 1x 2 -1 Reduces mod 2 to 0 1 1 1 0 1 0 0 1 7 Reflection through < 0 , 1 , 0 ,> is conjugate to 1 -1- 1x 1 0 -1 0- 1x 0 0 1 Reduces mod 2 to 1 1 1 0 1 0 0 0 1 8 Reflection through < 0 , 0 , 1 ,> is conjugate to 1 0 -1+ 1x 0 1 0+ 1x 0 0 -1 Reduces mod 2 to 1 0 1 0 1 0 0 0 1 9 Reflection through < 1 , 0 , 1 ,> is conjugate to -1+ 1x 2+ 1x -2- 1x 0+ 1x 2 -1 -2 1+ 1x 0- 1x Reduces mod 2 to 1 0 0 0 0 1 0 1 0 10 Reflection through < 1 , 1 , 0 ,> is conjugate to 1 0 0 0- 1x -1 1 0 0 1 Reduces mod 2 to 1 0 0 0 1 1 0 0 1 11 Reflection through < 1 , 0 , -1 ,> is conjugate to 1- 1x -1 1+ 1x 0- 1x 0 1+ 1x 2 -1- 1x 0+ 1x Reduces mod 2 to 1 1 1 0 0 1 0 1 0 12 Reflection through < -1 , 1 , 0 ,> is conjugate to -1 0 1- 1x 0+ 1x 1 -1- 1x 0 0 1 Reduces mod 2 to 1 0 1 0 1 1 0 0 1 13 Reflection through < -1- 1x , 1 , 1 ,> is conjugate to 1 0 0 0 1 0 1+ 1x 1 -1 Reduces mod 2 to 1 0 0 0 1 0 1 1 1 14 Reflection through < 1 , -1- 1x , 1 ,> is conjugate to 0+ 1x 1- 1x 0 1+ 1x 0- 1x 0 -1 1 1 Reduces mod 2 to 0 1 0 1 0 0 1 1 1 15 Reflection through < -1- 1x , -1 , 1 ,> is conjugate to 2+ 1x 0- 1x -1 2 -1- 1x 0+ 1x 1+ 1x 0- 1x 0 Reduces mod 2 to 0 0 1 0 1 0 1 0 0 16 Reflection through < 1 , -1- 1x , -1 ,> is conjugate to 1 0 0 1 0 -1 1 -1 0 Reduces mod 2 to 1 0 0 1 0 1 1 1 0 17 Reflection through < -1- 1x , 1 , -1 ,> is conjugate to -2- 1x -1+ 1x 1- 1x -2 1+ 1x 0- 1x -1- 1x -1 2 Reduces mod 2 to 0 1 1 0 1 0 1 1 0 18 Reflection through < -1 , -1- 1x , 1 ,> is conjugate to 1- 1x -2- 1x 2+ 1x -1- 1x -1 2 1 0- 1x 1+ 1x Reduces mod 2 to 1 0 0 1 1 0 1 0 1 19 Reflection through < 1 , -1 , -1- 1x ,> is conjugate to -1- 1x 0 2+ 1x -1 1 1 0- 1x 0 1+ 1x Reduces mod 2 to 1 0 0 1 1 1 0 0 1 20 Reflection through < 1+ 1x , 1 , 1 ,> is conjugate to -1 2+ 1x 0 0 1 0 -1- 1x 0+ 1x 1 Reduces mod 2 to 1 0 0 0 1 0 1 0 1 21 Reflection through < 1 , 1+ 1x , 1 ,> is conjugate to 0 0+ 1x -1- 1x -1 1+ 1x -1- 1x -1 0+ 1x 0- 1x Reduces mod 2 to 0 0 1 1 1 1 1 0 0