Non-Euclidean spaces are spaces that do not satisfy all of Euclid’s postulates. An example of such a space is hyperbolic space. In this paper, a method is discussed to draw a tessellation of hyperbolic space in a manner that fits with the virtual reality game "Holonomy", a game which takes place in hyperbolic space. The main result shows that the new approach is better in terms of simplicity than the old approach and is able to draw the game world more faithfully than the old approach. The features of the new approach could still be significantly expanded upon.