# polytope

polytope either converts a set of vertices to a set defining a polytope (in a lifted space), or converts a polytopic set to an MPT polytope

## Syntax

```
P = polytope(v,x)
P = polytope(M)
```

## Example

The native YALMIP use is for defing a polytope \(x = \sum_{i=1}^N \lambda_i v_i, \lambda \geq 0, \sum_{i=1}^N \lambda_i = 1\) from a set of vertices \( v_i\).

```
v = randn(2,10);
x = sdpvar(2,1);
P = polytope(v,x)
```

The opeprator does not perform any convex hull computation to reduce the numer of vertices. Note also that the polytope is defined in the \(x,\lambda\)-space. Hence, if you want plot it, you are most likely interested in the projection to \(x\)

```
plot(P,x)
```

The command also serves as the interface between YALMIP objects and MPT objects, allow us to convert objects. To generate a polytopic MPT object, simply apply the operator on a purely linear object.

```
x = sdpvar(2,1);
P = polytope([-1 <= x <= 1]);
```