A pyramid was a three-dimensional structure composed of four or five sides composed of (usually) triangular shapes.
The great pyramids of Egypt of Earth, such as the Great Pyramid of Giza, (TV: The Daleks' Master Plan et al) were well known to other races.
One splinter of Scaroth claimed to have caused the pyramids to be built, (TV: City of Death) though the Doctor was sceptical of this claim. (PROSE: A History of Humankind) The Osirans also influenced the building of the pyramids, and other pyramids were definitely constructed by 'aliens'. (TV: Pyramids of Mars, PROSE: Dead Romance) Osiran war missiles were pyramid-shaped and used "pyramid power". (TV: Pyramids of Mars)
Khepren supervised the construction of a pyramid. (TV: The Daleks' Master Plan)
The Exxilons influenced not only the Egyptian, but also the Aztec pyramids during their visits to Earth. (PROSE: The Left-Handed Hummingbird)
Anubian spacecraft had a pyramid shape. (TV: Curse of Anubis)
In a timeline where all of history was happening at once, Area 52 was housed inside a pyramid. (TV: The Wedding of River Song)
The Rings of Akhaten also had a pyramid, a holy site for the Sun-singers of Akhet, seven planets orbiting the same star, all of them sharing the belief that life in the universe originated on that pyramid. In it was a mummy. (TV: The Rings of Akhaten)
The Monks came to Earth in a pyramid from where they could manipulate their simulated worlds. (TV: The Pyramid at the End of the World)
The Great Intelligence used a three-sided pyramid constructed from Yeti control spheres as its physical form, though it truly had no physical form, (TV: The Abominable Snowmen) and it used such a geometry for a machine able to absorb the Doctor's mind. (TV: The Web of Fear)
When showing Adric the chameleon circuit of his TARDIS, the Fourth Doctor demonstrated that he could disguise the TARDIS as a pyramid, including a door so they could get in and out. (TV: Logopolis)
The Rani's TARDIS on Lakertya was disguised as a pink pyramid. (TV: Time and the Rani)
Peri Brown reminds the Sixth Doctor that their TARDIS had also materialized as a pyramid once, "on the frozen plans of Ewa Nine". (TV: Vengeance on Varos)
The Eleventh Doctor took Kazran Sardick and Abigail Pettigrew to visit the pyramids of Egypt on one of the Christmases he and Kazran visited Abigail. (TV: A Christmas Carol)
Sarah Jane Smith sabotaged a NASA probe from discovering a pyramid on Mars. (TV: The Vault of Secrets)
In 1977, Brigadier Lethbridge-Stewart investigated an Inca pyramid in South America. (AUDIO: The Cloisters of Terror)