Shape Grammar - Spatial Relationship between Tetrahedron + Pyramid

Hi all,

I'm currently studying some basic Shape Grammar in MIT. Worked on a small project exploring the emergence nature by a single spatial relationship between a perfect tetrahedron and a pyramid.

Tetrahedron: 24 Symmetries

Pyramid: 8 Symmetries

Design space = 24 X 8 = 192 permutations

So I decided to write a simple orientation script to iterate over all permutations. And this is the result. Below are some technical notes.

• I used the vertices of the shapes for creating a 3 point plane, and used it for orientation. 
• I used compound transform to combine multiple steps of transformation.
• The cross reference component is very handy, generating all the possible combinations without worrying too much about data tree.

The spatial relationship and the basic grammar A -> A + B and B -> A + B

The basic grammar and possible marker positions.

All results in 6 iteration steps

All results in 6 iteration steps (Top View)