Structure of the 3-dimensional cube tilings

• Orbit 1 has a stabilizer of order 384 and second moment 68921/8
• Orbit 2 has a stabilizer of order 32 and second moment 68301/8
• Orbit 3 has a stabilizer of order 64 and second moment 68101/8
• Orbit 4 has a stabilizer of order 16 and second moment 67491/8
• Orbit 5 has a stabilizer of order 128 and second moment 67301/8
• Orbit 6 has a stabilizer of order 16 and second moment 33843/4
• Orbit 7 has a stabilizer of order 128 and second moment 68081/8
• Orbit 8 has a stabilizer of order 32 and second moment 67281/8
• Orbit 9 has a stabilizer of order 48 and second moment 16769/2