The pure lineage of Omar Ibn Sahaak

Muhammad ibn Sa'ib al-Kalbi has reported in a book titled ‘al-Salaba fi Ma'rifat al-Sahaba’ (vol. 3, p. 212): “A slave boy named Nufail belonged to Lu’ayy bin Ghalib al-Qurashi. When Lu’ayy bin Ghalib al-Qurashi had passed away, Abdul Muttalib took care of the slave boy Nufail.  Sahak (a slave girl) used to shepherd Abdul Muttalib’s sheep. Abdul Muttalib used to separate Sahak from Nufail in the pasture and made Sahak wear a leather chastity belt with a lock and kept the key to himself.

“When the slave boy Nufail had seen Sahak in the grazing field, he fancied her and seduced her into having a sexual intercourse with him, so Sahak said: “I have no way of fulfilling what you want because of this chastity belt which only Abdul Muttalib has a key to” to which Nufail replied: “do not worry as I can get it off”. Subsequently, he grabbed some butter and grease and began to work it through the leather belt and her skin until it slid to her thighs.

“Nufail coupled with Sahak and as a result Sahak became pregnant with al-Khattab. After she had given birth to the boy, she left him around one of the nearby rubbish sites at night out of fear of Abdul Muttalib. Subsequently, the boy was picked up by an old Jewish lady named Janazah and was raised by her. When al-Khattab grew up, he became a woodcutter. While he used to be out cutting wood Sahak would check up on him while hiding. However, one day Khattab saw her bottom despicably revealed, while not knowing who she was he coupled with her.

"As a result, Sahak became pregnant with Hantama. When she had the girl, she left her near a rubbish site in Makkah. The girl was later picked up by Hisham ibn Mughira and raised by him. When she had grown up, al-Khattab fancied her as he used to often visit Hisham. As a result, al-Khattab asked for her hand in marriage from Hisham. Hisham married Hantama to Khattab and they had Umar."

So Basically:

Saahak got together with Nufeyl and brought "Khattab"
Then Khattab with Saahak and brought "Hantamah"
And then Khattab with Hantamah they brough "Umar".

So Hantamah would be the mother of Umar and his sister (from one father: Khattab).
And his Untie Hantamah and Khattab from the same mother: Saahak, therefore considered as brother/sister, and she is also the daughter of Khattab from Saahak, and his sister from their mother Saahaak.

And Khattab would be the father of Umar and his uncle (who is the brother of his mother Hantamah from Saahaak). And also Khattab is Umar's grandfather because he is the father of his mother Hantamah who brought him from Saahaak.

We conclude from all that:
- Khattab married (or got together) with his sister and brought Umar.
- Khattab married his daughter and brought Umar.
- Khattab is the father of Umar, his Uncle, and Grandfather.
- Hantamah is Umar's mother, his untie, and sister.

Umar can call his father: Dad, uncle, and grandfather.
Umar can call his mother: Mum, sister, and Untie.