@Kitonum It seems your method is more general in that the conditions within the map clause can be any that the programmer desires e.g. the cap could have an elliptical shape.

@Rouben Rostamian  Thanks, your procedure will help me in my current project. I believe my azimuth and polar are equivalent to your longitude and colatitude.

@vv Thanks to you my Maple education continues.

@vv Your programming here is amazing!

Unfamiliar with recursion, I can't see how Apollo ends. In particular how can the final display command execute apparently without the preceding gen(1,2,3,4) command executing for the second time?

@Carl Love Calling a Mobius strip single-edged reveals my almost total lack of knowledge of topology. The Catalan surface seemed different because it has two cusp-like edges between curved portions of the surface.

Thanks to you, I looked up the definition of homeomorphic in Wikipedia and am now just slightly less naive with topology!

@Kitonum This is good information. Thank you.

@vv Thank you!

Setting one of the two surface variables, beta, to its constant range limits, as you did above, displays a spacecurve on the surface's curved edge.

Repeating p2 with alpha set to its constant range limits displays the surface's horizontal straight line edges.

What criteria determine which surface variable in the spacecurve will display the curved edge?

What is displayed when your technique is applied to a single edge minimal surface such as a Mobius strip?

@acer Thank you Acer. I believe Maplesoft should simply add a color parameter to the title and caption plot parameters.

@Kitonum Thank you, Kitonum, but why can't Maplesoft simply add a color parameter to the title and caption plot options?

@Kitonum As do often in the past, you've given me a new insight.

@Kitonum A brilliant answer! Please explain.

@acer Thank you for these displays. It is enlightening to view the one with range m = 0..1 first along the t axis, then along the m axis.

@Carl Love Thanks to you and vv I believe I now understand the graph.

@vv Is this correct?

For each value of m on the graph, the y coordinate is the maximum for all real values of t, which value does not appear.

Could Maple create a plot of a 3D surface where, for each surface point, the x and y coordinates are m and t and the z coordinate is the maximum?

@vv Based on your hints, I will spend some time investigating.