The worksheet below contains an example of the tiling of the hyperbolic plane.

I would like to produce this and other hyperbolic plane tilings from Maple worksheets, but I don't know the math technique for doing so.

Please direct me to a source of the requisite knowledge or an example worksheet which I can study and imitate.

Hyperbolic_Plane_Tiling.mw

I create a table of 3D points in one worksheet and would like to use these values at a later time in a separate worksheet.

What is the simplest way to do this?

This worksheet produces a very strange error.

I have examined every assignment and cannot find one which relates to the error message.

Can anyone help here?

Strange_Error.mw 

This worksheet displays an ellipsoid internally tangent to the four sides of a tetrahedron.

The tetrahedron is a special case: it has a horizontal base with vertices A,B and C and its fourth vertex E is on the z axis.

However I have failed when trying to display an internally tangent ellipsoid in any other tetrahedron.

Will any tetrahedron support one or more internally tangent ellipsoids?

If so, are there conditions restricting the location of the mutual points of tangency?

Ellipsoid_in_a_tetrahedron.mw

In this worksheet the solve command almost immediately gives up and DirectSearch[SolveEquations] is erratic.

For some triangle/inellipse points of tangency the latter provides a nonsense answer and for others it produces an almost correct solution.

Is there a set of conditions which determine the possibility of an inellipse within a triangle?

Inellipse.mw

A responder will have to establish a connection to the DirectSearch package.