Omar Khayyam made significant contributions to the creation of the Jalali calendar, which was a major achievement in Islamic astronomy and Persian culture. Here are the key aspects of his contributions:

1. Leadership and Collaboration: Khayyam led a team of eight scholars under the patronage of Sultan Malik-Shah. Together, they conducted extensive astronomical observations and revised astronomical tables to ensure the calendar's accuracy.

2. Astronomical Precision: Khayyam's team recalibrated the calendar so that the first day of the year coincided with the vernal equinox, marking the beginning of spring and the Nowruz celebration. This alignment was crucial for the calendar's solar basis.

3. Intercalation System: The Jalali calendar introduced a unique intercalation cycle, which included a combination of quadrennial and quinquennial leap years. This system helped maintain the calendar's accuracy over time.

4. Accuracy Compared to Other Calendars: The Jalali calendar is noted for its high accuracy, with an error of only one day every 5,000 years, surpassing the Gregorian calendar's error rate of one day every 3,330 years.

5. Legacy and Impact: The Jalali calendar was used in Greater Iran from the 11th to the 20th centuries and influenced later calendar reforms. It became the official national calendar of Qajar Iran in 1911 before being simplified in 1925 to form the modern Iranian calendar.