---------------------------------------
Domain:
         - Q + 3S  -5 >= 0
         P -3S + 8 >= 0
         - R + 3S  -5 >= 0
         P - R  >= 0
         Q + R -3S + 1 >= 0
          1 >= 0

Vertices:
[ S-1,  -Q+3S-4 ]
[ Q/3+2/3 ,  1 ]
[ S-1,  3S-8 ]
[ 2,  1 ]

Ehrhart Polynomial:
( -1/6 * Q^2 + ( 1 * S + -7/6 )
 * Q + [ ( -3 * S + 5 )
, ( -3 * S + 16/3 )
, ( -3 * S + 5 )
 ]_Q )

---------------------------------------
Domain:
         - Q + 3S  -5 >= 0
         - P + 3S  -8 >= 0
         P - R  >= 0
         Q + R -3S + 1 >= 0
          1 >= 0

Vertices:
[ S-1,  -Q+3S-4 ]
[ Q/3+2/3 ,  1 ]
[ S-1,  P ]
[ 2,  1 ]
[ P/3+5/3 ,  P ]

Ehrhart Polynomial:
( -1/6 * P^2 + ( 1 * S + -13/6 )
 * P + [ ( -1/6 * Q^2 + ( 1 * S + -7/6 )
 * Q + [ ( -3/2 * S^2 + 7/2 * S + -2 )
, ( -3/2 * S^2 + 7/2 * S + -5/3 )
, ( -3/2 * S^2 + 7/2 * S + -2 )
 ]_Q )
, ( -1/6 * Q^2 + ( 1 * S + -7/6 )
 * Q + [ ( -3/2 * S^2 + 7/2 * S + -5/3 )
, ( -3/2 * S^2 + 7/2 * S + -4/3 )
, ( -3/2 * S^2 + 7/2 * S + -5/3 )
 ]_Q )
, ( -1/6 * Q^2 + ( 1 * S + -7/6 )
 * Q + [ ( -3/2 * S^2 + 7/2 * S + -2 )
, ( -3/2 * S^2 + 7/2 * S + -5/3 )
, ( -3/2 * S^2 + 7/2 * S + -2 )
 ]_Q )
 ]_P )

---------------------------------------
Domain:
         Q -3S + 5 >= 0
         P -3S + 8 >= 0
         - R + 3S  -5 >= 0
         P - R  >= 0
         S  -3 >= 0
         R  -1 >= 0
         Q + R -3S + 1 >= 0
          1 >= 0

Vertices:
[ S-1,  1 ]
[ S-1,  3S-8 ]
[ 2,  1 ]

Ehrhart Polynomial:
( 3/2 * S^2 + -13/2 * S + 7 )

---------------------------------------
Domain:
         - P + 3S  -8 >= 0
         Q -3S + 5 >= 0
         P - R  >= 0
         R  -1 >= 0
         Q + R -3S + 1 >= 0
          1 >= 0

Vertices:
[ S-1,  1 ]
[ S-1,  P ]
[ 2,  1 ]
[ P/3+5/3 ,  P ]

Ehrhart Polynomial:
( -1/6 * P^2 + ( 1 * S + -13/6 )
 * P + [ 0, 1/3, 0 ]_P )

