The screenshot shows two polytopes and its Minkowski sum and is obtained by the following commands:

	P=cube(3);
Q=ball(3);
R=P+Q;
plot(P);
plot(Q);
plot(R);

There are different options to enter a convex polyhedron:

V-representation: Finitely many points, for example $$0 \choose 3$$, $$3 \choose 0$$, $$2 \choose 2$$, and finitely many directions, for example $$-1 \choose 0$$, $$0 \choose -1$$, are stored column-wise, respectively, in a field V and a field D of a structure rep:

	rep.V=[0 3; 3 0; 2 2]';
rep.D=[-1 0;0 -1];

 A polyhedron P is defined, where option 'v' indicates that rep is a V-represenation. The result is plotted:  P=polyh(rep,'v'); plot(P); 

H-representation: A polyhedron P of the form $P=\{x \in \mathbb{R}^n |\; a \leq Bx \leq b,\; l \leq x \leq u\}$ is considered. For example, an H-representation for $P=\{x \in \mathbb{R}^2 |\; 2 \leq 2 x_1 + x_2,\; 2 \leq x_1 + 2 x_2,\, x_1 \geq 0\}$ can be enererd as

	clear rep;
rep.B=[2 1; 1 2];
rep.a=[2; 2];
rep.l=[0; -Inf];

 A polyhedron Q is defined, where option 'h' indicates that rep is an H-represenation. The result is plotted:  Q=polyh(rep,'h'); plot(Q); 

 Another calculus example: The intersection of P and Q is computed and stored in R. The result is plotted:  R=P&Q; plot(R); 

 The Cartesian product of P and Q is computed and stored in S. The image of the 4-dimensional polyhedron S under the ($$3 \times 4$$)-matrix M is a 3-dimensional polyhedron T with 5 vertices and 4 extremal directions. The length of the unbounded edges in the plot is set to 10:  S=P:Q; M=[2 1 3 8; 1 6 8 5; 1 7 5 0]; T=S.im(M); opt.dirlength=10; plot(T,opt); 

Many other examples can be found in the reference manual.