# Sierpinski Dodecahedron

By: Gijs Bellaard

## Description

The Sierpinski dodecahedron is made by repeatedly replacing the 20 corners of all the dodecahedron with half-sized dodecahedron.

## GLSL Code

```
//The golden ratio
const float PHI = 1.61803398875;
//The amount of iterations
const int ITERATIONS = 15;
//The scaling factor between iterations
const float SCALE = 1. + PHI;
//Fold normals
const vec3 N1 = normalize(vec3(-1.0 , PHI-1.0 , PHI ));
const vec3 N2 = normalize(vec3(PHI-1.0, PHI , -1.0 ));
const vec3 N3 = normalize(vec3(PHI , -1.0 , PHI-1.0));
float distanceSierpinskiDodecahedron(vec3 p){
float s = 1.;
for(int i=0; i<ITERATIONS; i++){
//Folds
p -= 2.*min(0.,dot(p,N1))*N1;
p -= 2.*min(0.,dot(p,N2))*N2;
p -= 2.*min(0.,dot(p,N3))*N3;
p -= 2.*min(0.,dot(p,N2))*N2;
p -= 2.*min(0.,dot(p,N1))*N1;
p -= 2.*min(0.,dot(p,N2))*N2;
p -= 2.*min(0.,dot(p,N3))*N3;
//Scaling
p *= SCALE;
s *= SCALE;
//Offset
p -= 1.;
}
//Distance to a dodecahedron
float d = distanceDodecahedron(p);
return d/s;
}
```