#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "l.h"
//This generates an icosohedron.
R el, e=0.00000001;
R wh[12][3]; int whp = 0;
static R sq(R x){return x*x;}
static void mp(R x, R y, R z){wh[whp][0] = x; wh[whp][1] = y; wh[whp++][2] = z;}
static void mpx(R x, R y, R z){mp(x, y, z); mp(y, z, x); mp(z, x, y);}
static void mpy(R x, R y, R z){mpx(x, y, z); mpx(x, y, -z); mpx(x, -y, z); mpx(x, -y, -z);}
static int nr(int i, int j){R s=0; int u=3; while(u--) {s += sq(wh[i][u]-wh[j][u]);
       if(s>el+e) return 0;}
   if(s<el-e) exit(printf("%d %d %e %e Poo\n", i, j, s, el));
   if(0) printf("nr %20.15f\n", s);
   return 1;}
short tp[20][3];
bp g3(){el = sq(sqrt(5)-1);
int wtp = 0;
mpy(0, 1, (sqrt(5)-1)/2);
if(0) {int j; for(j=0; j<12; ++j) printf ("zz %d %9.5f %9.5f %9.5f\n",
        j, wh[j][0], wh[j][1], wh[j][2]);}
{int i=12; while(i--) {int j=i; while(j--){int k=j; while(k--){
   if(nr(i, j) && nr(i, k) && nr(j, k)) {
      R det = wh[i][0]*(wh[j][1]*wh[k][2] - wh[j][2]*wh[k][1])
            + wh[i][1]*(wh[j][2]*wh[k][0] - wh[j][0]*wh[k][2])
            + wh[i][2]*(wh[j][0]*wh[k][1] - wh[j][1]*wh[k][0]);
   if(0) printf("za %d %d %d %20.15f\n", i, j, k, det);
   if(wtp == 20) exit(printf("Pot\n"));
   tp[wtp][0] = i; if(det>0) {tp[wtp][1] = j; tp[wtp++][2] = k;}
                        else {tp[wtp][1] = k; tp[wtp++][2] = j;}}}}}}
   if(0) {int q=20; while(q--) printf("[%2d; %2d; %2d];\n", tp[q][2], tp[q][1], tp[q][0]);}
   return (bp){3, 12, (R*)wh, 20, (short *)tp};}

R const wht[][3] = {{1, 1, 1}, {-1, -1, 1}, {-1, 1, -1}, {1, -1, -1}};
short tpt[][3] = {{1, 2, 3}, {0, 2, 1}, {0, 3, 2}, {0, 1, 3}};
bp g3t(){return (bp){3, 4, (R*)wht, 4, (short *)tpt};}