al-waqt

‘Umar ibn al-Khattaab (d. 644 CE – radiyallahu ‘anhu) (Link 1)
I first read about Polyphasic sleeping from an Islamic message board that was talking about how ‘Umar ibn al-Khattaab used to sleep this way, and this is when he was the ruler of the entire Muslim world. He is paraphrased as saying, “If I sleep in the morning, I’ll lose the entire Muslim world (given the fact that he was busy being the leader of a nation which was in the process of conquering half the world), and if I sleep at night I’ll lose myself (as in that sleeping at night will cause him to not worship Allah as much as needed).”

Imaam an-Nawawi (d. 1278 CE – rahimahullah) (Link 1, Link 2)
Another example of a dynamic and beneficial person in Islamic history is Imaam an-Nawawi. His pursuit of knowledge dominated his entire life. He would put all of his time into studying, learning, and teaching. It is even stated that he would not sleep except when sleep would overtake him. He would rest on his book and sleep for a little, then he would act startled upon awakening and continues studying. He once said about himself, “I spent two years without lying on the ground [to sleep] on my side.” That is, he would always study and write until sleep overtook while in a sitting position. Al-Qutb al-Yauneeni said about him, “He would not waste any moment of the day or night but he would spend it busy with attaining knowledge. Even when he walking and in the streets he will be busy going over what he had remembered and reviewing his notes. He continued gaining knowledge in that way for a period of six years.”

It seems – and only Allah knows the reality – that Allah truly blessed his time. Perhaps this was due to a sincere intention to please Allah. As mentioned above, he would attend up to twelve classes a day. Commenting on that fact, al-Diqr wrote,

He used to have twelve study sessions a day with his teachers. These included explanations, verifications, commentaries, explaining the different aspects and expressions as well as exacting the correct wordings. This would take, at a least approximation, twelve hours a day. Then he would need to review what he had learned and memorise what need to be memorised. The very least approximation is that this would also take twelve hours a day. This is twenty-four hours in a day! When would he sleep? When would he eat? When would he perform the acts of worship? When would he perform the voluntary late night prayers? It is well-known that he performed those types of acts of obedience and worship. When would all of that take place? He was in need of studying and reviewing for all the twenty fours in a day and night. This shows how Allah blessed and graced this man. Allah blessed him in his time. He gave him the ability to complete in one day what it takes everyone else two years to accomplish. This is the only way we can explain this tremendous undertaking that made him one of the greatest scholars of his time in about ten years. In fact, it made him the leader (Imaam) of his time. This is also the only way we can explain all of his wonderful, detailed and radiant writings in a span of time that lasted no more than fifteen years. He spent all of his lifetime and living hours in learning, teaching and writing.

And Imaam an-Nawawi died at 45 years old!