Pyramidion

The Pyramidion is a Vex stronghold located in Echo Mesa, Io. It is only accessible during the Strikes The Pyramidion and The Festering Core, and the Curse of Osiris story mission Deep Storage. It is the lair of Brakion, Genesis Mind.

Overview
According to Ikora Rey and Asher Mir, the Pyramidion on Io is one of many; every Vex machine world has a Pyramidion, and these structures serve as the Vex's main machinoforming engines. It is also believed that all Pyramidions are intrinsically connected to each other and lead to the same interior space. On at least one occasion, this interior appeared markedly different than was previously recorded, suggesting that it is either capable of reconfiguring its structure or that a Pyramidion may actually lead to one of several common spaces.

The Pyramidion is also noted to contain massive repositories of information, far more than most normal Vex facilities are capable of. It possesses Warp Gates inside the leads to thousands of places and realities. Ikora had the Guardian search for a map within the facility that depicted all possible realities within the Infinite Forest, in order to locate Panoptes, Infinite Mind.

Asher's Accident
"So, what can we expect from this place?" "A cascading hellscape of infinite change. My fireteam required dozens of resurrections on our expedition." "And I'm sure it was uphill both ways to the lake where you lost your arm." "You waste my time with a vapid joke, but, yes! Paradoxically, it was."

- Ghost, Asher and Ikora

Sometime after the events of The Taken King, just before Eris Morn's departure from the Tower, Asher and his fireteam of two Hunters set off to explore the Vex structure on Io. They quickly found themselves outmatched by the machines, dying and being resurrected time and time again until they reached a radiolarian lake located deep within. Watching his teammates being torn apart by the Vex, Asher began to scramble for a way out, when suddenly a tentacle caught his Ghost and he felt pain in his shoulder--and then he lost consciousness.

When he woke up, he found his right arm had been transformed into a Vex one - a process apparently irreversible, possibly lethal, and still advancing. Desperate to find both answers and a cure, Asher settled in the Rupture on Io to study the machines which had maimed him and fantasise of revenge he would one day have.

Brakion's End
"This is about simple vengeance, assistant. Brakion the Genesis Mind converted my arm and changed my life forever. I want it dead."

- Asher Mir

Deep Storage
"If the Vex are trying to reshape the future, the Pyramidion is part of the plan."

- Ikora Rey

The Festering Core
"Zavala. This whole sphere is a dedicated processing structure. A giant Vex computational array." "What could the Taken want with a Vex computer?"

- Ghost and Zavala

Pyramid over the Pyramidion
"If the Darkness claims the Pyramidion, it will dissect it for study. Unfold its innumerable dimensions, wade through its multitudinous seas radiozoic, peer through its crackling warp gates leading toward a million millions of new realities…"

- Asher Mir

Years later, following the Pyramids' return and the landing of one such entity over Io, Asher noticed the Darkness was most likely watching the Vex. After conducting studies along with his assistant the Guardian, he concluded the Darkness wished to claim and dissect the Pyramidion for study. Repulsed by this prospect, he vowed he would not let it come to pass, readying to personally defend the structure had something come out of the Pyramid and assailed it.

Having refused Zavala's proposal of evacuating to the Last City, Asher acted on his promise and entered the Pyramidion once more. He traversed it, wrecking havoc to all Vex he encountered along the way, until they stopped attacking him and retreated to watch his every move. When he arrived at the shores of his radiolarian lake, he found it suspended above where the sky should be - and reaching with both of his arms, he brought it down.

Trivia

 * In the Transcript of the Pyramidion Strike, it is described to be a Hilbert Space, the concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. Considering that it is described as an infinite dimensional functional space would lean towards the latter, even Ikora stated that entering the Pyramidion is the same as transcending the physical reality.
 * It also mentions us climbing through a Sierpiński Carpet which is one of the Fractals of the Hausdorff Dimension, which the former behaves as a higher-dimensional space in terms of how much space it takes up in a topological dimension.
 * And followed by going through a Manifold, which is either a pipe or chamber branching into several openings, or in mathematics, a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analog of this in three or more dimensions.
 * Also mentions with our eigenstate in the Pyramidion coordinates, which is a quantum-mechanical state corresponding to an eigenvalue of a wave equation. which eigenvalue is each of a set of values of a parameter for which a differential equation has a nonzero solution (an eigenfunction) under given conditions.
 * A Vex structure in the background of the Crossroads Crucible map appears to be the the Mars Pyramidion. Of note is that Crossroads is set in a region of Mars known as the Lost Oasis, which bears resemblance to the location on Io of the same name.

List of appearances

 * Destiny 2
 * Curse of Osiris
 * Shadowkeep
 * Season of Arrivals