# Equation to a rectangular Prism

1. May 21, 2014

### michael pranit

Hello,
I am trying to understand the concept of solid geometry(spheres, cubes, polyhedra etc) as a function of their co-ordinates.
for example, the general ellipsoid, is a quadratic surface which is given in Cartesian coordinates by:
(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1
a,b,c being the semi axis.
-Is there an equation to a rectangular prism as a function of the x,y,z coordinates like the ellipsoid?
Could someone clarify/explain.
Any help will be appreciated.
Thank you

2. May 21, 2014

### Matterwave

The rectangular prism is the the sum of 6 planes. Do you know the equations for planes?

3. May 21, 2014

### HallsofIvy

Staff Emeritus
Because a "rectangular prism" is not smooth (it has edges and corners) you cannot give it as one differentiable function. You can, as Matterwave suggests, write equations for each of the six planes.

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