Food4Rhino

Horta is a Grasshopper component library for the implementation of the Space Groups and the International Notation System used to define them in design computation.

The Space Groups are the 230 combinations of symmetry operations and elements in three dimensions.

The International Notation System is the most common system for accessing the Space Groups, popular within crystallography. It is used here because the system is readable by both humans and machines, and so provides concise and precise instruction sets to directly link design intention, execution of the computation, and description of the physical assemblies.

One advantage of this system is its structure: it maintains the index at which each unit cell, sub-unit, or transformation can be located throughout all component operations.

Horta does not require mathematical expertise. Each description consists only of a crystal system and cell centering, and a three-part International System symbol. Horta provides all of these in readable form, alongside instructions to interpret any information specific to a group.

Currently Horta provides all of the parallelepiped Crystal Systems (Triclinic, Monoclinic, Orthorhombic, Rhombohedral, and Cubic). A forthcoming update will provide the Trigonal and Hexagonal systems. It provides flexible means for constructing all of the space groups based on these Crystal Systems so that the designer can access these Discrete assemblies, but focus their on design, not math. It strives to give ample feedback so that the designer does not need to be an expert in the space groups to use them.

Future additions are: the component to define the Trigonal and Hexagonal systems, a numerical Space Group selector component, and the glide plane symmetry logic. All other elements of the Space Groups are currently included.

(Paraphrased from the paper by the developer found here.)