Nikah Halala

“COITION mujama’a-t; nikah; nik
Francis J. Steingass, English-Arabic Dictionary: For the Use of Both Travellers and Students, W.H. Allen, 1882

NIKAH - Literally the act of sexual intercourse, nikah is the term by which marriage is referred to in the Qur'an. Islamic law defines nikah as a civil contract whose main function is to render sexual relations between a man and woman licit.
The New Encyclopedia of Islam: Third Edition, Altamira, 2001

Nikah halala is one of the most bizarre and revolting aspects of Islamic law. Nikah means sexual penetration, and halala means to make something halal, or permissible. This type of Nikah is based on Quran, Surah Al-Baqarah, verse 230 and Hadith Sahih Bukhari, volume 7, book 72, number 715.

Quran, Surah Al-Baqarah, verse 230
So if a husband divorces his wife ˹three times˺, then it is not lawful for him to remarry her until after she has married another man and then is divorced. Then it is permissible for them to reunite, as long as they feel they are able to maintain the limits of Allah. These are the limits set by Allah, which He makes clear for people of knowledge.

Hadith Sahih Bukhari, vol. V, Book 72, no. 715
"Narrated Ikrima: 'Rifaa divorced his wife whereupon Abdur-Rahman married her. Aisha said that the lady came wearing a green veil and complained to her (Aisha) and showed her a green spot on her skin caused by beating. It was the habit of ladies to support each other, so when Allah's messenger came, Aisha said, "I have not seen any woman suffering as much as the believing women. Look! Her skin is greener than her clothes! When Abdur-Rahman heard that his wife had gone to the prophet, he came with his two sons from another wife. She said, "By Allah! I have done no wrong to him, but he is impotent and is as useless to me as this," holding and showing the fringe of her garment. Abdur-Rahman said, "By Allah, O Allah's messenger! She has told a lie. I am very strong and can satisfy her, but she is disobedient and wants to go back to Rifaa." Allah's messenger said to her, "If that is your intention, then know that it is unlawful for you to remarry Rifaa unless Abdur-Rahman has had sexual intercourse with you." The prophet saw two boys with Abdur-Rahman and asked (him), "Are these your sons?" On that Abdur-Rahman said, "Yes." The prophet said, "You claim what you claim (that he is impotent)? But by Allah, these boys resemble him as a crow resembles a crow.""

Sunan Abi Dawud 2309
Narrated Aisha, Ummul Mu'minin: The Messenger of Allah (ﷺ) was asked about a man who divorced his wife three times, and she married another who entered upon her, but divorced her before having intercourse with her, whether she was lawful for the former husband. She said: The Prophet (ﷺ) replied: She is not lawful for the first (husband) until she tastes the honey of the other husband and he tastes her honey.