Is There an Equation for a Rectangular Prism in Cartesian Coordinates?

[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

 

[Matterwave]

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

 

[HallsofIvy]

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.