Geometry of the settlement

The Honeycomb Conjecture.

During a presentation at the 2014 ISDC, when he was asked how important the shape of a spacecraft is, Aldo Spadoni jokingly answered that, given enough rockets, anything can fly.

The shape and geometry are, without a doubt, the two most defining features of the settlement. Every other aspect, such as life on board, engine power and even the prospect of artificial gravity are strongly influenced by the outline of the spacecraft. Therefore, choosing the shape is terms of design and functionality.

The Honeycomb Space Settlement follows in the steps of nature and takes after the honeycombs built by bees. In geometry, a two-dimensional honeycomb is a hexagonal tiling (tessellation) of the Euclidian plane, in which three hexagons meet at each vertex (also called a hextille). The internal angle of the hexagon is 120 degrees so that any three hexagons at a point make a full 360 degrees.

The two properties of a honeycomb which make it suitable for this application are as follows:

1 . The hexagonal tiling is the densest way of arranging two-dimensional circles. 2 . Dividing a surface into regions of equal area using hexagonal tessellation yieldsthe least total perimeter per region. [1]

Out of the two theorems, the most relevant one is the latter. Known as the Honeycomb Conjecture, it was first recorded in 36BC and was proven in 1999 by mathematician Thomas C. Hales. What the conjecture tells us is that for any given settlement area, hexagons are the most efficient shape in terms of material consumption. This is highly important, seeing that the current price of taking one kilogram into space is several thousand dollars. In order to keep the settlement relatively affordable for world governments and/or private space agencies, all unnecessary costs must be brought to a minimum.

Fig. 1.1 hexagonal lattice Fig. 1.2 densest circle packing

Even without taking engineering and geometry into account, one can still argue that the hexagon is the most appropriate shape for our settlement, for it suits the minimalistic philosophy behind our project perfectly. Drawing inspiration from the honeycomb let us create a simple yet highly upgradeable modular design, making the colony entirely plausible with today’s technology. In our quest for finding exactly how small such a spacecraft can get, the hexagon shines through as the best candidate.

Structuring the settlement as a lattice made out of individual modules brings along several advantages over other designs. The lattice allows engineers to build new hexagonal cells both on Earth, as well as in situ, facilitating the construction process and making sure that all deadlines are met. Furthermore, advanced safety measures can be easily implemented and each cell can work autonomously, acting as a hybrid between a miniature settlement and a traditional spaceship. However, the biggest advantage will always be the reduced size resulting in the most efficient use of resources. This brings us to our next stop, which is the economic and social aspect of building our spacecraft.