# Concept of a 3D-Printed Voronoi Egg-Shaped Habitat for Permanent Lunar Outpost
## 1 Introduction
Among the main goals of creating the concept of the 3D-printed habitat for permanent lunar outpost was to explore ways of depositing the habitat both on the surface of the Moon and in the craters. Furthermore, the way to ensure safe and relatively comfortable entrance to the habitat by the most direct route possible, through the pressurized room was also analysed. In the next phase of conceptualisation, properties of the egg-shaped habitat (and its realization) were of key interest. Due to low lunar gravity, astronauts are forced to move on the Moon by small jumps instead of ordinary walking. Taking this fact into consideration, one should come to the conclusion that the shape of the future lunar base should have more of a vertical than horizontal shape. The vast majority of proposals of future lunar bases harness the shape of the traditional dome. This type of structure is very efficient on Earth but is questionable on the Moon. People who are walking on Earth need structures which provide \"horizontal space\". On the Moon, astronauts will need much more \"vertical space\". In authors' opinion egg-shaped habitat would provide more vertically focused space which would be much more practical to use by astronauts. Of course, it is necessary to ensure the lightness of the structure and proper (from architectural and ergonomic points of view) layout of the internal space. Another problem that long-term (or permanent) missions will face with is the danger of radiation and falling meteorites. Therefore, variants using inflatable membranes that would be covered with regolith were analysed as a possible solution. Greenhouses with the possibility of growing plants have become another focus for sustainable accommodation. In this regard, several variants have been created, which include a transparent membrane [16], and use mirrors to direct and regulate light radiation into an otherwise covered and therefore protected environment [17]. In order to create lunar habitats, it is necessary to provide components which could be used to rise such structures characterised by sufficient mechanical strength. The most common construction material on the Earth is concrete which, in its simplest form, consists of aggregate, water, and cement. On the Moon, there is a possibility to create alternatives. The most promising seem to be sulphur concrete [18] and geopolymers [19; 20; 21]. 3D printing technology is the cornerstone of the extra-terrestrial construction, which involves harsh and remote locations and very limited resources [22]. Geopolymer, as a type of non-conventional construction material, is one of the options with the greatest potential for implementation in lunar civil engineering 3D technology [23]. Additionally, sulphur concrete is one of the options for lunar construction programme. Sulphur as a binding agent is readily available on the Moon, no water is needed for the concrete production, and it can be produced under cold temperatures [22]. 3D printing gives a unique opportunity to create complicated structures such as Voronoi structures. [PERSON] was a mathematician of Ukrainian descent living at the turn of the 19 th and 20 th centuries, famous for extending a diagram also known as Dirichlet tessellation. A Voronoi diagram is, in the simplest case, a partition of a plane into regions close to a given set of objects called seeds (see Figure 1). Voronoi diagram decomposes an area or a volume into smaller pieces, and each resulting Voronoi cell consists of the points that are closest to the given Voronoi site [24]. If the seeds are placed in a 3D space, the partition is limited to the fixed space. One of the most significant advantages of using a Voronoi structure is to save material while maintaining mechanical properties. The Voronoi structure provides a reduction in stiffener mass up to 67% [25]. A Voronoi diagram has many applications in many fields of science and art. One of the earliest uses of this tool was the analysis of the cholera epidemic in London, which occurred in 1854.