Question: Caliph Al-Hasan ibn ‘Ali is the grandson of which Islamic prophet? 

Context articles: Sheikh Sharaf ad-Din ibn al-Hasan
Burial place of Fatimah
Family tree of Muhammad
Sultan Ali
Ali al-Asghar ibn Husayn
Al-Hakim I
Fakhr ad-Din ibn Adi
Ali al-Akbar ibn Husayn
Mujtaba
Zaynab bint Ali

Shaykh Sharaf ad-Dīn ibn al-Hasan, known also by the Yazidi name " Sherfeddin", was a descendant of Umayyad Caliph Marwan ibn al-Hakam.
 He was the son and religious heir of al-Hasan ibn ‘Adī and thus head of the ‘Adawiyya Ṣūfī Order.
 He died in battle against the Mongols in 1258 and was succeeded by his uncle, Fakhr ad-Dīn ibn ‘Adī.
The burial place of Fatimah is a disputed issue among different sects of Muslims.
 Fatimah was a daughter of the Islamic prophet (Arabic: نَـبِي‎ ‎ ) Muhammad and Khadijah (therefore, a member of Muhammad's "Bayt" (Arabic: بَـيـت‎ ‎ , 'Household')), wife of ‘Ali ibn Abi Taleb, and mother of Al-Hasan and Al-Husain, It is said that ‘Ali buried his wife in an unknown location, according to Fatimah's decision with the aim of expressing her anger towards the caliph of the time.
 Different locations have been mentioned as the possible burial place of Fatimah.
 Some of them are said to be nearer to fact: Al-Baqi', her house and between the Muhammad's tomb and his minbar.
This article is about the family tree of the Islamic prophet, Muhammad.
 He was known as a member of the family of Hashim and the Quraysh tribe which is ‘Adnani.
'Ali ibn Muhammad ibn 'Ali ibn al-Husayn was the son of the fifth imam of Twelver Shii Muslims and fourth imam of Ismaili Shii Muslims, Muhammad al-Baqir.
 Born in Medina, 'Ali, known in Iran as "Sultan 'Ali," was dispatched by his father to the areas of Kashan and Qom, where he served as a Friday prayer leader and teacher; his popularity and his preaching of Shii Islam proved threatening to the local representative of the Umayyad dynasty.
 The Umayyad representative's forces cornered and killed Sultan 'Ali and a band of his supporters, after a prolonged battle, and before a larger group of supporters could arrive, in Ardahal, a village roughly 45 kilometers east of Kashan on August 7, 734 CE (27 Jamadi II, 116 AH).
 He is still revered by Shii Muslims, especially in Iran, where his burial place—which has undergone repeated renovations but dates, in part, to the Saljuq period—has become a site of visitation.
 The shrine is known for a distinctive annual carpet-washing ritual ("qālī-shūyān") that occurs on the seventeenth day of autumn to commemorate the day of Sultan 'Ali's martyrdom, a ritual that might have its origins in Sultan 'Ali's body having been wrapped in a carpet and brought to the site of his burial after his murder.
‘Abdullah ‘Ali al-Asghar ibn Al-Husayn (09 Rajab 60 AH – 10 Muharram 61 AH (10 October 680 CE)), or simply ‘Ali Asghar ("Younger ‘Ali"), was the youngest child of Al-Husayn (son of ‘Ali, grandson of the Islamic Prophet Muhammad and the third Shia Imam) and Rubab bint Imra’ al-Qays.
 He was martyred during the Battle of Karbala’, and is commemorated in Shi‘ism as the "personified quintessence of the innocent victim."
Al-Hakim I (Arabic: الحاكم بأمر الله الأول‎ ‎ ) Abu al-'Abbas Ahmad ibn Abi 'Ali al-Hasan held the position of the Abbasid Caliph of Cairo, Mamluk Egypt for the Mamluk Sultans between 1262 and 1302.
 He was an alleged great-great-great grandson of the Abbasid Caliph al-Mustarshid, who had died in 1135.
 When Baghdad fell to the Mongols in 1258, al-Hakim I escaped to Damascus where he befriended the Arab tribal chief 'Isa ibn al-Muhanna, who tried to set him up as caliph, but in the confusion surrounding the Mongol invasion of Syria in 1259-1260, he ended up in Aleppo, where he was proclaimed.
 However, the much closer and probably genuine uncle of the last Abbasid caliph al-Musta'sim, al-Mustansir II, was proclaimed caliph in Cairo in 1261.
 Al-Hakim I joined al-Mustansir II's invasion of Iraq, also submitting to al-Mustansir II as caliph, but the latter was slain with most of the invaders near Hīt in Iraq by the Mongols.
 Only about fifty troops escaped with al-Hakim, who, making his way back to Cairo and after a careful scrutiny of his genealogical claim to be an Abbasid, was proclaimed caliph in succession to al-Mustansir in 1262.
 Since al-Hakim's connection with the Abbasids is distant and faint, it cannot now be known whether he was really from that family as he claimed or not.
 In any case, al-Hakim I had no further adventures, served as a legitimating and ceremonial functionary for the Mamluk sultans in Cairo, reigned for thirty-nine years, and became the progenitor of all the subsequent Abbasid caliphs of Cairo, whether he was really an Abbasid or not.
 Although he was kept in office after 1262, the Mamluk sultans kept him as a virtual prisoner in the citadel, until Sultan Lajin released him in December 1296, allowing him to live in a house in the city and giving him a bigger financial emolument.
Shaykh Fakhr ad-Dīn ibn al-Hasan, known also by the Yazidi name "Şêx Fexreddin", was a descendant of Umayyad Caliph Marwan ibn al-Hakam.
 He was the son and religious heir of al-Hasan ibn ‘Adī after the death of al-Hasan's son.
 Şêx Fexreddin was the seventh and last known ‘Adawī shaykh, leaving the Lalish area (and the historical record) for the Yazidish-founded Ayyubid Egypt in 1276.
‘Ali al-Akbar ibn Al-Husayn (Arabic: علي الأكبر ابن الحسين‎ ‎ ), or simply "Ali al-Akbar," was the son of Al-Husayn ibn ‘Ali, the third Shi‘ite Imam, and Umme Layla.
 He was killed at the age of 18, 19 or 25 on the day of ‘Ashura’, in Karbala’.
 ‘Ali Al-Akbar is also highly respected by Sunni Muslims.
 According to Jean Calmard writing in Iranica, ‘Ali al-Akbar's reputation as a valiant warrior of the Household of Muhammad might have preceded that of Al-‘Abbas ibn ‘Ali.
Al-Mujtaba (Arabic: اَلْـمُـجْـتَـبَى‎ ‎ ) is an Arabic word which means "The Selected One" or "The Chosen One among many."
 It is a title of the Islamic "Nabi" (Arabic: نَـبِي‎ ‎ , Prophet) Muhammad, and his grandson, the Caliph Al-Hasan ibn ‘Ali.
Sayyidah Zaynab bint ‘Ali (Arabic: الـسَّـيّـدة زَيـنـب بـنـت عـلي‎ ‎ , Also: 'Zainab') was one of the daughters of the fourth Sunni caliph and the first Shia imam, ‘Ali and his first wife Fatimah.
 The Islamic "Nabi" (Arabic: نَـبِي‎ ‎ , Prophet) Muhammad was her maternal grandfather, and thus she is a member of his "Bayt" (Arabic: بَـيـت‎ ‎ , Household).
 Therefore, she is often revered not only for her admirable characteristics and actions, but also for her membership in, and continuation of, the biological line of Muhammad.
 Like other members of her family she became a great figure of sacrifice, strength, and piety in Islam – in the Sunni and Shi‘i sects of the religion.
 Zaynab married ‘Abdullah ibn Ja‘far, and had three sons and two daughters with him.
 When her brother, Imam Al-Husain, stood up against Yazid ibn Mu‘awiyah in 680 CE (61 AH), Zaynab accompanied him.
 She played an important role in protecting the life of her nephew, Imam ‘Ali ibn Al-Husayn, and because of her sacrifice and heroism, she became known as the "Heroine of Karbala’".
 Zaynab died in 681 CE, and her Masjid is located in Damascus, Syria, Ash-Sham.