Questions: a user-centric world map puzzle - user picks the starting point

[dakra]

I am a cartographic newb, trying to develop a user-centric world map puzzle that lets the user decide which place is the starting point and which pieces that could be adjacent are laid out contiguously.

My current thinking is to have all pieces be equal size hexagons, or approximately a hexagon, with slightly curved or jagged edges to avoid duplication, like on a Myriahedral Projection. Each piece would be the central portion of a projection.

I want to make this freely available, so GNU or Creative Commons software and data are fine.

Once I calculate the centers for each piece, I'd like to be able to automate the production of each piece from map data, cropping to the desired shape, saving as a graphic file, etc, probably in python. I'm starting with QGIS.

Questions:
(1) Is this an inherently bad idea?
(2) Has this been done already? Pointers, please.
(3) Is there a different free software package than QGIS that would better suit my needs?
(4) Any recommendations on which projection to use for each piece?

I would prefer the following attributes, in descending importance:

• Equidistant: Distances from the center of each piece to other places on the same piece are correct to scale.
• Azimuthal: Great circles through the center of each piece are represented by straight lines on the piece,
• Gnomic: All great circles are straight lines.
• All the above, across multiple adjacent pieces.

I am sure that some of these desired attributes are mutually exclusive or not possible across multiple pieces. but don't know what the incompatibilities are.
Advice will be appreciated.

[Falconius]

To number 1, all ideas are inherently bad, they only get good if people work on them and bring them to fruition.
2: No idea but it sounds pretty original.

I'm not sure how having unique edges on the pieces helps you. If you do that, the map has to be arranged in a particular way, no? Is it a puzzle or is it freeform? I'm not sure I really understand the core concept.

Other than that it sounds like a lot of programing and math stuff which there are definitely those around here to help with.

[dakra]

Thank you for the words of wisdom and the encouragement.
re:

having unique edges on the pieces

All the pieces would be shaped the same. The edges might be jagged, but fit with its adjacent partner, like unrolled gears. Top left edges on any piece could align with bottom right edges on any other. Alternatively, they could be regular hexagons, with little blank areas along the edge, like in a Myriahedral Projection.

re:

sounds like a lot of programing and math stuff which there are definitely those around here to help with

I can deal with lots of programming. Math stuff like spherical geometry, I am learning. I would prefer to exploit what is already in the applications and extensions, rather than reinvent unnecessarily.