03-27-2021, 02:57 PM
(This post was last modified: 03-27-2021, 03:07 PM by dale walton.)

Simply by name, eg:

(board (polyhedron Icosahedron))

You can go wild with which polyhedra to include.

I doubt games with more complications than named polyhedra are needed, by if so the next step could be something like

(board (net Symmetry:{2 3 5} using:(tri 3)))

(board (net Symmetry:{3 3 3 3} using:(square 2)))

(board (net Symmetry:{3 5 3 5} using:(square 3))) -- i.e. Tricontrahedron with tic-tac-toe faces

-- and then people can remove points they don't want...

(board (net Symmetry:{ {2 2 2} {2 2 2 2}} using:{(tri 2) (square 2)} )) ?? snub cude with divided faces.... not sure this works,,,

Maybe:

(board (net Symmetry:{2 3 5} using:{(tri 3) axes:{5 5 5}} ))

(board (net Symmetry:{2 3 4} using:{{(tri 2) axes:{2 2 2}} {(square 2) axes:{2 2 2 2}}} ))

I think that is still the future and you may have better ideas...

The display axis must be centered on a face in order to a avoid sites at infinity. -- so no option for polyhedra with a single type of face -- or perhaps center:<cell>. Get a math student to work out the formulas to locate the center of the face and the node points as projected on the plane, as the polyhedra are divided with duals and diagonals, etc.

Only for play on nodes of grid. (If for faces, an orthogonal projection with rotation utilities would be appropriate, but hard to implement and hard to play.)

The actual projections probably need to be determined by experiment. Curved connections would look best, but stereographic may have too great a difference in scale: you could try an azimuthal equidisdant projection instead.

(board (polyhedron Icosahedron))

You can go wild with which polyhedra to include.

I doubt games with more complications than named polyhedra are needed, by if so the next step could be something like

(board (net Symmetry:{2 3 5} using:(tri 3)))

(board (net Symmetry:{3 3 3 3} using:(square 2)))

(board (net Symmetry:{3 5 3 5} using:(square 3))) -- i.e. Tricontrahedron with tic-tac-toe faces

-- and then people can remove points they don't want...

(board (net Symmetry:{ {2 2 2} {2 2 2 2}} using:{(tri 2) (square 2)} )) ?? snub cude with divided faces.... not sure this works,,,

Maybe:

(board (net Symmetry:{2 3 5} using:{(tri 3) axes:{5 5 5}} ))

(board (net Symmetry:{2 3 4} using:{{(tri 2) axes:{2 2 2}} {(square 2) axes:{2 2 2 2}}} ))

I think that is still the future and you may have better ideas...

The display axis must be centered on a face in order to a avoid sites at infinity. -- so no option for polyhedra with a single type of face -- or perhaps center:<cell>. Get a math student to work out the formulas to locate the center of the face and the node points as projected on the plane, as the polyhedra are divided with duals and diagonals, etc.

Only for play on nodes of grid. (If for faces, an orthogonal projection with rotation utilities would be appropriate, but hard to implement and hard to play.)

The actual projections probably need to be determined by experiment. Curved connections would look best, but stereographic may have too great a difference in scale: you could try an azimuthal equidisdant projection instead.