Generating Tikz codes from Sage for drawing scattering points in 3D ...

[Jimmy Lee]

I am a beginner in Sage and Tikz, and have written the following snippet of Sage code:

P = Polyhedron(ieqs=[(30, -2, -2, -1), (25, -1.5, -2, -3),(20,-2,-1,-1), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)])
pts = P.integral_points()
point3d(pts,rgbcolor=(1,0, 0), size=10) + P.plot(rgbcolor = 'yellow', opacity = 0.5)

The purpose of the codes is to generate the integral points interior to the polytopes bound by 6 inequalities as given in the codes. The output is the following.

However, I tried to following the following reference:

    http://doc.sagemath.org/html/en/thematic_tutorials/polytope_tikz.html

to generate Tikz codes for LaTeX and failed. Unlike Polyhedron which is a kind of object that can respond to "projection", point3d generates only a Graphics3D object which doesn't understand "projection".

Is there any way to output these points to Tikz as well?

Also, is it possible to ask Sage to color each of the facets of the polytope in different colors (just like Tikz can)?

Many thanx in advance!

[HG]

I used a lot tikz/circuitikz but with new version of sage 8 (and before I think too) it doesn't work so smoothly.
A the moment I use %%tikzmagic ( https://github.com/robjstan/tikzmagic/blob/master/example.ipynb )
and https://github.com/mkrphys/ipython-tikzmagic/blob/master/tikzmagic_test.ipynb
but they are problems. For example,

%%tikz --scale=0.5 --border=10 works this way but if you write --scale 2 it doesn't work.
And many commands have to be changed or don't simply work.
At the moment I do geometry with sage, it's long but quiet pretty, 
but if I could mixed both sage and tikz would be sometimes better