# Sierpinski Icosahedron

By: Gijs Bellaard

## Description

The Sierpinski icosahedron is made by repeatedly replacing the 12 corners of all the icosahedron with half-sized icosahedron.

## 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 = 2.;
//Fold normals
const vec3 N1 = normalize(vec3(PHI, 1.0-PHI, -1.0 ));
const vec3 N2 = normalize(vec3(1.0, PHI , -PHI-1.0));
//Offset
const vec3 O = vec3(-0.850650787,-0.525731087,0);
float distanceSierpinskiIcosahedron(vec3 p){
float s = 1.;
for(int i=0; i<ITERATIONS; i++){
//Folds
z = abs(z);
z -= 2.*min(0.,dot(z,N1))*N1;
z -= 2.*min(0.,dot(z,N2))*N2;
//Scaling
z *= SCALE;
s *= SCALE;
//Offset
z += O;
}
//Distance to a icosahedron
float d = distanceIcosahedron(p);
return d/s;
}
```