# How to plot the equation |x|+|y|+|z|=1 ?

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Jes on 30 Jan 2017
Commented: Walter Roberson on 30 Jan 2017
I have a 3D equation. Can anyone help me to plot this? Thanks

Benjamin Kraus on 30 Jan 2017
Edited: Benjamin Kraus on 30 Jan 2017
If you are using MATLAB R2016b you can use the new fimplicit3 command:
fimplicit3(@(x,y,z) abs(x)+abs(y)+abs(z)-1)
You may also be interested in fplot, fplot3, fsurf, fmesh, fcontour, and fimplicit (some of these have been available since R2016a, but fimplicit3 was added in R2016b).
Walter Roberson on 30 Jan 2017
Nice solution, Benjamin!

John Chilleri on 30 Jan 2017
Edited: John Chilleri on 30 Jan 2017
Hello,
I'm certain there's a better way to do this, such as with surf, but here is a solution.
If you consider the equation, you realize that it's all planes joined by the 6 vertices {(1,0,0),(0,1,0),(0,0,1),(-1,0,0),(0,-1,0),(0,0,-1)}. These 6 vertices 'form' 8 sides.
Using the fill3 command, you can reconstruct the shape:
fill3([1 0 0],[0 1 0],[0 0 1], 'r')
hold on
fill3([1 0 0],[0 1 0],[0 0 -1], 'r')
fill3([1 0 0],[0 -1 0],[0 0 -1], 'r')
fill3([-1 0 0],[0 -1 0],[0 0 -1], 'r')
fill3([-1 0 0],[0 -1 0],[0 0 1], 'r')
fill3([-1 0 0],[0 1 0],[0 0 1], 'r')
fill3([-1 0 0],[0 1 0],[0 0 -1], 'r')
fill3([1 0 0],[0 -1 0],[0 0 1], 'r')
which results in the following image:
(This is just an angle I chose to show.)
Hope this helps!
John Chilleri on 30 Jan 2017
If you are running R2016b, Benjamin Kraus has the smart solution! I'm running R2015b, and I would encourage my solution only if you are running an older release.

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