As usual the actual grave is below a much larger room, the man is looking into the former, trough an opening.

The name of this tomb is somewhat of an enigma. I took the name from the plaque one can see on some of the pictures. On Google one can find Sadrettin Konevi Türbesi, whereas the street is called the Saadettin Konevi Sokak. I think it's wisest to stick to the plaque. I could not read more, but it must be a Seljuk type tomb. I also found that in Konya there is a tomb of about the same name, but that is later and in a totally different style.
Adding in 2024: In an article about the Karanlık Kümbet (an alternative name) by Abdüsselam Uluçam it is stated (condensed Google translation): “According to its inscription, it was built by Sadreddin Türkbeg in 708 (1308). The tomb, which was ruined over time, was repaired by the General Directorate of Foundations in 1954. Although it is recorded in the Erzurum Province Yearbook that Sadreddin Konevi was buried here, this is not true. The Dark Tomb has the same features as the tomb monuments built during the Seljuk and Ilkhanid periods in Anatolia. The star-shaped inscription, thought to be the signature of the master, is repeated exactly on the dome of Tercan Mama Hatun Tomb and Beyşehir Eşrefoğlu Mosque.”