Tesseract is a term to describe an area in space warped across multiple dimensions. A person who can create and navigate tesseracts is likened to a three-dimensional entity interacting with the second-dimension; while still limited by gravity, they can nonetheless perform remarkable feats such as moving through solid matter, transiting vast distances and literally turning space inside-out. Due to the massive power requirements, few are capable of harnessing the energy needed to create tesseracts. However, species such as the Pocket Universe species, the Magog, Celestial Avatars, and the Vedrans have shown some ability to do so. It should be noted that the Pocket universe species had to harness the entire energy output from a galaxy, while the Vedrans tesseracted the Ral Parthia solar system with Voltarium cannibalized from a Nova bomb.
In reality, a tesseract is a hypercube, a four-dimensional ($ n^4 $) cube. If a person could get to the fourth dimension, they would indeed be able to navigate common three-dimensional space the same way we can perceive the second dimension.
Portable Tesseract GeneratorEdit
The Portable Tesseract Generator (PTG) appeared in "Into the Labyrinth". Satrina Leander and her assassin team each had 1 inserted into their dataports. It allowed them to terrorize the diplomatic meeting of the charter signatories and be invulnerable to weapons fire.
Rommie described it to Harper thus, "A person who could create and navigate tesseracts would be like a 3 dimensional being interacting with the second dimension. Now they'd still have to worry about gravity, but they could move through solid matter, transit vast distances, even turn space inside out."
Seamus Harper eventually traps Satrina, removes her PTG and inserts it into his own Dataport in an attempt to remove the Magog larvae in his stomach. When this fails he begins to become possessed by the Abyss, yet he overcomes by not giving in and instead sabotages Satrina's ship, which is powering all the PTG's. At the last moment he removes the PTG from his dataport and throws it across the room. A flash of electrical discharge goes through it as well as the assassins, causing them to be in flux and able to be defeated.
Alice String Tesseract GeneratorEdit
Seamus Harper has been taking medicine to keep the Magog larvae in his stomach dormant. The medicine is no longer working and he has a week to live before they begin to hatch and kill him. In a desperate attempt to remove the larvae, Dylan contacts the Perseids, technical director Hohne and his assisstant Rakeeb and they join Harper to work on the Alice Strings and Tesseract Machine (ASTM). They are using the Tesseract Generator Harper confiscated from Satrina Leander in "Into the Labyrinth" and modifying it with Perseid technology.
Since they barely understand the extent and power of the Spirit of the Abyss' technology all hell breaks loose on the Andromeda Ascendant by shifting time and space all over the ship. Eventually, it starts causing massive disturbances on Xinti.
It causes temporal flux from a future, where they had completed the machine, but they can't stop the temporal disturbances because Hohne took the liberty of assembling several miniature robots to begin the assembly process and they cannot find their way to the machine shop. Hohne falls into the Slipstream Core and is presumed dead, but he actually falls into a Tesseract and reappears in "Through a Glass Darkly".
Finally, the gold Trance Gemini activates the ASTM and saves Harper's life. This action locks her in their timeframe and eliminates the spatial distortions.