Vectors in 3 Dimensions

Mathematical background

In mathematics a vector has a magnitude (length) and direction expressed as an ordered list of tuples (x, y, z). It is sketched as a directed line segment (arrow). Unless otherwise given, a vector does not impart information about location (when studying in secondary education, we use the origin (0,0,0) of a set of axis as the initial point of a vector.

The tetrahedron has the smallest number of faces in the five Platonic Solids, having only 4 faces. And in fact, four faces are the minimium requirement for a polyhedron. Other features of tetrahedron includes:

• Each face is an equilaterial triangle
• Each vertex is the meeting of 3 faces

Introduction

Platonic solids are polyhedron which satisfy 3 conditions

1. all its faces are congruent convex regular polygons,
2. none of its faces intersect except at their edges, and
3. the same number of faces meet at each of its vertices

Hexahedron

The most commonly recognised platonic solid, also known as a cube. 

All of my projects to date have required step by step instructions (some upwards of 300 lines of code!), so I decided to have a go at working out how to create a recursive code. After studying "Cayley graph 3D" working out in my head how the code was constructed, I was finally able to start my own. The following is based on an image of 

Cayley Graph of the Free Product Z₃ * Z₅

_{After much trial and error I was able to develop ...}