public class TriangleTwo
{
    private static int[] edg= new int[12];
    private static int[] tri = new int[8];
    private static int[] cub = new int[4];
    private static int total;
    private static int[] edgTotal = new int[13];
        
    public static void main(String [] args)
    {                  
        total = 0;
        
        for(int i = 0; i < 12; i++)
            edgTotal[i] = 0; 
        
        for(int i = 0; i < 12; i++)
            edg[i] = 0; 
               
        for(int i = 0; i < 4096; i++)
        {
            total = total + checkTri();            
            
            addModTwo(edg,0);            
        }
        
        System.out.println("Total possibilities: " + total);            
        
        for(int i = 0; i < 13; i++)
            System.out.println("Possibilities with " + i + " 'zero' edges: " + edgTotal[12 - i]);
    }

    public static void addModTwo(int[] a, int i)
    {
        if(a[i] == 0)
        {
            a[i] = 1;
            return;
        }
        
        else if(i > 10) return;
        
        else
        {
            a[i] = 0;
            addModTwo(a,i+1);           
        }
    }    

    public static int checkTri()
    {
        tri[0] = edg[4] + edg[5] + edg[8];
        tri[1] = edg[0] + edg[1] + edg[6];
        tri[2] = edg[6] + edg[7] + edg[8];
        tri[3] = edg[2] + edg[3] + edg[7];
        tri[4] = edg[3] + edg[4] + edg[11];
        tri[5] = edg[1] + edg[2] + edg[10];
        tri[6] = edg[9] + edg[10] + edg[11];
        tri[7] = edg[0] + edg[5] + edg[9];
                       
        for(int i = 0; i < 8; i++)
            if(tri[i] == 1) return 0;            
        
        if(!checkCubic()) return 0;
        
        int edges = 0;
        
        for(int i = 0; i < 12; i++)
            edges = edges + edg[i];
                
        edgTotal[edges]++;
        
        return 1;
    }
    
    public static boolean checkCubic()
    {
        cub[0] = (edg[5] * edg[1] * edg[3]) - (edg[2] * edg[4] * edg[0]);
        cub[1] = (edg[6] * edg[4] * edg[10]) - (edg[11] * edg[1] * edg[8]);
        cub[2] = (edg[5] * edg[10] * edg[7]) - (edg[2] * edg[8] * edg[9]);
        cub[3] = (edg[6] * edg[3] * edg[9]) - (edg[11] * edg[0] * edg[7]);
        
        for(int i = 0; i < 4; i++)
            if(cub[i] != 0)
                return false;
                       
        return true;      
    }
}
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