# Forming a solid from a set of intersecting planes

suppose I have equations of planes in 3D space in the form:

$A_ix + B_iy + C_iz = D_i$ for some values of i

**how can use sage to find the solid enclosed by them?** I need a plot of the surface of this solid. Actually I have many such sets of planes each forming a solid like this.(all concentric)

**For example:**

planes at x = -1, 1 in yz plane; planes at y = -1, 1 in xz plane and planes at z = -1, 1 in xy plane intersect and form a unit cube centred at the origin.

ty ndomes! But, its taking very long. I have like 12 or more equations (seen a maximum of 30 but can be more). I am now thinking of a different approach. We can easily make a function:

```
def inside(point , planes):
if the point is inside all the planes:
return 1
else:
return 0
```

so, now is there a good function in sagemath that can show all the region in space for which f(point) gives 1. (yea, its okay if the solids are filled as long as they're transparent enough. . Naively Taking lots of points and finding this solid(Like monte carlo) is very inefficient

Actually the program is taking very long time for these equations.

```
[-x - y - 1 == 0, -x - z - 1 == 0, -x + z - 1 == 0, -x + y - 1 == 0, -y- z - 1== 0, -y + z - 1 == 0, y - z - 1 == 0, y + z - 1 == 0, x - y - 1== 0, x - z - 1 == 0, x + z - 1 == 0, x + y - 1 == 0]
```

so, check it once. Thanks!