Proxima Centauri

Proxima Centauri is a small, low-mass red dwarf star located 4.24 light-years away from Sol in the constellation of Centaurus. Proxima Centauri is a member of the Alpha Centauri star system, being identified as component Alpha Centauri C, and orbits the AB pair at roughly 12,950 AU with a period of about 550,000 years. It was humanity's first target for exploration and colonization outside of their home system and where they first encountered sapient alien life.

Eurytion
Eurytion, being tidally locked to Proxima Centauri, has a day as long as its year, which is to say eleven Earth days long. Native Centaurians measure these days by the movement of stars in the night sky of the cold, outward-facing hemisphere, particularly that of Alpha Centauri A.. For Centaurians, the position of the sun in the sky and the passage of time have no correlation, instead it varies depending on one's position on Eurytion's surface. On the inward-facing hemisphere there is a point where Proxima Centauri hang directly overhead.

Eurytion's proximity to Proxima Centauri has caused volcanism across its surface from tidal flexing, although its extremely stable, circular orbit has moderated this. The gasses emitted by volcanoes have helped Eurytion's atmosphere recover from its star's frequent bouts of violent weather, while the heat keeps the outward facing hemisphere habitable, if still bitterly cold outside these islands of warmth and perpetually dark. The strong tidal forces exerted on it have also held its axial tilt to an obliquity of 0°, meaning there are no seasons on either hemisphere or the narrow terminator line separating them. This consistency in weather and temperature may have enabled life to first emerge in the moderate conditions of the terminator line.

Eurytion formed close to Proxima Centauri and during the red dwarf's tumultuous youth, when the habitable zone was much further out and lost much of the water it had started with. Luckily a late bombardment of icy asteroids came after the star cooled and shrunk, giving Eurytion back water and permitting life to evolve.

The Hippodamia Cylinders
The Hippodamia Cylinders were constructed at Eurytion's Lagrange 4 point to house both humans and Centaurians together despite their physiological differences. To achieve this, the two massive cylinders tethered together at their ends and forever rotating out from each other where segmented into three levels, the innermost being Earthlike, the outermost being like Eurytion's terminator line and the middle being a compromise between the two. The immense cost and scale of the artificial habitat was justified given the significance of humanity's discovery of alien intelligence.