The Headless Pyramid, otherwise identified as Lepsius XXIX or Steinpyramide XXIX, is the remain of a pyramid complex built in Saqqara. The identity of the pyramid owner is unclear, though it is suspected to belong to either pharaoh Menkauhor of the Fifth Dynasty or pharaoh Merikare of the Tenth Dynasty, both of whom are known to have built a pyramid. If associated with Menkauhor, the pyramid's name is either Nṯr-ỉswt Mn-kꜣw-ḥr meaning 'Divine are the places of Menkauhor' or Nṯr-ỉswt Ỉkꜣw-Ḥr meaning 'Divine are the places of Ikauhor' referencing Menkauhor's birthname; if associated with Merikare, the pyramid's name is Wꜣḏ-swt Mry-kꜣ-rꜥ meaning 'Fresh are the places of Merikare'. Other candidates for the pyramid owner that have been proposed are Amenemhat I of the Twelfth Dynasty and an ephemeral pharaoh Ity [de] of the Eighth Dynasty.

The pyramid complex is in very poor condition. Only the main pyramid, its substructure, and the mortuary temple can be definitively identified. Trace elements of a cult pyramid and a causeway exist, however, there is no sign of an extant valley temple. The base of the pyramid superstructure has been measured by various Egyptologists as being 52 m (171 ft; 99 cu), 60 m (200 ft; 110 cu), or 65 m (213 ft; 124 cu) by 68 m (223 ft; 130 cu) long. Its substructure was thoroughly investigated between 2005 and 2008 by a team of archaeologists led by Zahi Hawass. Their findings included lowered portcullis gates indicating a burial had taken place, a sarcophagus lid built of schist, and holes cut into the burial chamber floor presumed to have held canopic jars.

Karl Richard Lepsius visited the site in 1843, providing brief description and cataloguing it as 'Steinpyramide XXIX' in his pyramid list. Gaston Maspero entered the underground chambers in 1881, searching the ruins for evidence of Pyramid Texts. Alessandro Barsanti was active in Saqqara in 1900, clearing a section of the pyramid. A brief and unsystematic excavation of the ruins was conducted in 1930 by Cecil M. Firth. The most systematic investigation of the site was conducted between 2005 and 2008 by a team led by Zahi Hawass.

Old Kingdom mortuary complexes typically consist of five main components: (1) a valley temple; (2) a causeway; (3) a mortuary temple; (4) a cult pyramid; and (5) the main pyramid. The 'Headless Pyramid' has an identifiable main pyramid with substructure and a mortuary temple. There are scant remains of a presumed cult pyramid and causeway, but no trace of a valley temple. The complex is overall in very poor condition.

The pyramid had a base length of approximately 65 m (213 ft; 124 cu) by 68 m (223 ft; 130 cu) according to Celeste Rinaldi and Vito Maragioglio; a base length of approximately 60 m (200 ft; 110 cu) according to Lepsius; or a base length of approximately 52 m (171 ft; 99 cu) according to Firth. Virtually nothing remains of the superstructure, hence its local Arabic name of 'Headless Pyramid'. This pyramid was enclosed by an enclosure wall constructed from mudbrick.

The entrance to the substructure lies in the approximate middle of the pyramid's north face. The descending passage was probably 7.6 m (25 ft) long, though its original entrance point now lies under a house and thus cannot be completely excavated. The remains of the passage are limited, though it appears to have had a downward slope of 30° and a fine white limestone paving. The passage terminates into a hall 2.75 m (9.0 ft) north-south by 2.06 m (6.8 ft) east-west with fine white limestone-lined walls. Beyond the hall is a granite-lined passage sealed by two pink granite portcullises. The passage measures 5.6 m (18 ft) in length and had an estimated ceiling height of 3.8 m (12 ft), and the portcullis stones were found to be 0.5 m (1.6 ft) thick. The sealing of the passage indicates that a burial had been conducted. A second corridor 7 m (23 ft) in length then leads to the ante- and burial- chambers. The antechamber has been obliterated and retains no walls, but its size could be estimated by outlines left on the ground, indicating the chamber was 3.2 m (10 ft) long. The burial chamber is in markedly better condition allowing it to be measured as approximately 8 m (26 ft) east-west by 3.2 m (10 ft) north-south, with walls that reached a height of at least 4.15 m (13.6 ft), and a floor originally paved with fine white limestone. Inside the burial chamber, the intact lid of a sarcophagus made of grey schist was uncovered. The lid measured 2.65 m (8.7 ft) by 1.09 m (3.6 ft) and was found covering holes cut in the floor presumed to have held canopic jars. Finally, adjoining the antechamber is a presumed serdab though nothing but an outline of it remains, indicating a possible size of 3.85 m (12.6 ft) east-west by 3.2 m (10 ft) north-south.

The adjoining mortuary temple of the pyramid is known by its local Arabic name as 'Joseph's prison'. To the south, bounded by the enclosure wall, were the remains of another smaller building presumed to be the cult pyramid.

There are trace remains of a causeway leading towards the fertile ground east of the pyramid, though no trace of a valley temple has been uncovered.