$EXEC orbit
(0,1,2)(3,5,4)(8,9,10)(11,13,12)
(0,4)(1,5)(2,6)(3,7)(8,12)(9,13)(10,14)(11,15)
(0,2)(1,7)(3,5)(4,6)(8,10)(9,15)(11,13)(12,14)
(0,7)(1,2)(3,4)(5,6)(8,15)(9,10)(11,12)(13,14)
..
001000010011010001
001010000010001101
001110010010000010
001111000000010001
111010000000010100
001100000010111000
001011100011000000
111100000011000000
111000011100000000
110000000010000111