public class TrianglesOneThree
{
    private static int[] edg = new int[12];
    private static int[] tri = new int[8];
    private static int[] quar = new int[3];
    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[0] + edg[1] + edg[2];
        tri[1] = edg[2] + edg[3] + edg[5];
        tri[2] = edg[0] + edg[3] + edg[4];
        tri[3] = edg[1] + edg[4] + edg[5];
        tri[4] = edg[9] + edg[10] + edg[11];
        tri[5] = edg[7] + edg[8] + edg[11];
        tri[6] = edg[6] + edg[8] + edg[9];
        tri[7] = edg[6] + edg[7] + edg[10];
                       
        for(int i = 0; i < 8; i++)
            if(tri[i] == 1) return 0;            
        
        if(!checkQuartic()) return 0;
        
        int edges = 0;
        
        for(int i = 0; i < 12; i++)
            edges = edges + edg[i];
                
        edgTotal[edges]++;
        
        return 1;
    }
    
    public static boolean checkQuartic()
    {
        quar[0] = (edg[0] * edg[5] * edg[9] * edg[7]) - (edg[2] * edg[4] * edg[6] * edg[11]);
        quar[1] = (edg[0] * edg[5] * edg[10] * edg[8]) - (edg[1] * edg[3] * edg[6] * edg[11]);
        quar[2] = (edg[1] * edg[3] * edg[9] * edg[7]) - (edg[2] * edg[4] * edg[10] * edg[8]);
        
        for(int i = 0; i < 3; i++)
            if(quar[i] != 0)
                return false;
                       
        return true;      
    }
}
<br />
<b>Notice</b>:  (null)(): [ALERT] Mailbox is over quota in <b>Unknown</b> on line <b>0</b><br />