What is the distance between the sciatic nerve and the colon at the closest point?
Short answer
Sciatic nerve pain cannot be caused by a full colon.

background
The sciatic nerve runs at the back of the pelvis down the the leg. The sciatic nerve exits the spine from the lumbar spine to S3 in the sacrum (Fig. 1).  

 
Fig.1. Left: sciatic nerve overview. Right: Sacral plexus. Source: Manchester Bedford Clinic

Hence the sciatic nerve does not come into contact with the bowel and intestines located ventrally in the abdominal cavity (Fig. 2).


Fig.2. Left: sciatic nerve in detail showing dorsal location. Right: Intestines ventrally situated in abdominal cavity. Source: Manchester Bedford Clinic and University of Maryland

Pain in the sciatic nerve (sciatica) is often caused by compression or entrapment by muscles, tendons, and other soft tissues along the nerve path Manchester Bedford Clinic.