@Kitonum In my original question I omitted the role of density.

Does your answer (as corrected) assume a uniform density of one? How does your answer change if the truncated ellipsoid has a uniform density other than one?

@Kitonum Your answers are always clear.

@vv Your answers are always helpful.

@vv Thank you and I apologize.

I just realized that I used acceleration derivatives where the correct operations are velocity derivatives.

For interest sake, what do A and B represent in your reply?

@tomleslie 

ShadeVertical.mw

@tomleslie Thanks for your detailed reply.

1) I have removed command Picture which was left in the worksheet in error.

2) Several of the executions of procedure ConstructCircle give incorrect results in your PCTiling.mw. I do not know why.

    Here is a corrected version of Poincare_tiling. It executes with correct results this morning on my machine; I can only hope it does so for you as well.

If not, then perhaps all you can do for me, if possible, is to direct me to a source that I can learn from showing one or more implementions of the transformation formula.

Poincare_tiling.mw

@tomleslie I thank you first for the helpful observation and then for your detailed answer. 

It will take me some time to digest this and I may have follow-on questions.

I am new to hyperbolic geometry and only recently learned how to create a hyperbolic circle and a hyperbolic line through any two points in the Poincare disk. This is a fascinating branch of geometry!  

@tomleslie I can't remember why I drew my Poincare disk centred at [1,1].

Would shifting the disk and the points within it so the disk was centred at [0,0] help you or another respondent to provide an answer?

If yes, I will do so and resubmit my question. 

@mmcdara The extra "verbosity" in your reply gives me additional understanding.

@dharr Your reply helps  me progress in Stillwell's book.

@dharr Sorry for the delay in replying, somehow your email to me went to spam. 

@acer My table is a table data structure. Save and read work perfectly and seem to be the simplest way to share the table between worksheets.

@Joe Riel I fixed the unmarked comment and also applied Acer's fix to geom3d[point] and my worksheet executes properly.

@acer After applying your fixes my worksheet executes properly.

I'm glad you are available to help.

@mmcdara I'm out of town for a few days and then I will chase down the references you have mentioned and let you know what I find. 

Here is a worksheet showing an inellipsoid lying obliquely in a tetrahedron. It requires a link to the DirectSearch package.

Inellipsoid_in_a_tetrahedron.mw

I also have worksheets showing inellipsoids lying vertically and horizontally in a tetrahedron.