# Knoblauch's blog

## Octahedron

**O**ctahedron is the third platonic solid. It consists of 8 faces (each is an equilateral triangle) and 6 vertices (each at the meeting of 4 faces).

## Tetrahedron

**T**he 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

## Hexahedron

# Introduction

Platonic solids are polyhedron which satisfy 3 conditions

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

**Hexahedron**

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

## An attempt at using recursion

**A**ll 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 Z _{3} * Z_{5}**

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

## Snub dodecahedron

**T**he Snub dodecahedron has 92 faces (12 pentagons, 80 equilateral triangles), 150 edges, and 60 vertices.

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