WHILE TAXIING FOR TKOF AT NIGHT; AN ACR CAPT TAXIED ACROSS THE RWY ASSIGNED BY GND CTL. THE FO WAS CONSULTING THE ARPT DIAGRAM TO CONFIRM THE RTE AND HAD NOT HAD THE CHANCE TO INTERVENE. THE FO CITES FATIGUE AS THE MAIN CAUSE OF THE ERROR.

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TAXIING FOR TKOF IN OMAHA; CLRED TO TAXI TO RWY 35. AS WE APCHED A TURN ON THE TXWY THE CAPT SAID; 'WE ARE CLRED TO RWY 35; CORRECT?' I ANSWERED YES AND LOOKED DOWN AT THE TAXI CHART (ARPT DIAGRAM) TO CONFIRM OUR RTE. AS I LOOKED UP CAPT TAXIED ACROSS HOLD SHORT LINE TO CROSS THE RWY THINKING IT WAS RWY 32L. BY THE TIME I LOOKED UP I REALIZED WE CROSSED RWY 35. I TOLD THE CAPT HE JUST CROSSED RWY 35 AND I NOTIFIED GND CTL. THEY INSTRUCTED US TO TURN AROUND AND TAXI BACK TO RWY 35 AND SAID THERE WAS NO PROB WITH THE XING. I BELIEVE THE MAIN CAUSE OF THE ERROR WAS FATIGUE. BOTH PLTS COMMUTE AND HAD BEEN AWAKE APPROX 14 HRS AND THIS WAS THE FIRST LEG OF A 3 LEG; 9 1/2 HR DUTY PERIOD. WE STARTED OUT FATIGUED. I ALSO BELIEVE POOR ARPT MARKINGS ARE A CAUSE. IT IS VERY DIFFICULT TO NAV AND DISTINGUISH RWYS FROM TXWYS AT NIGHT. I ALSO THINK I SHOULD HAVE BEEN MORE AGGRESSIVE BECAUSE I WASN'T SURE WHERE WE WERE AND I SHOULD HAVE TOLD THE CAPT TO STOP UNTIL I OR WE WERE SURE WE WERE XING RWY 32L AND NOT RWY 35.