Template talk:Star polyhedron navigator

This list was split from Template:Convex polyhedron navigator

I'm not very sure about the usefulness of all these complicated named in one list. I'd prefer a visual list, even like a single bitmap with a matrix of pictures with a link mapping to each form, but don't know if you can do that in Wikipedia. Tom Ruen (talk) 03:00, 9 September 2009 (UTC)

I think you can do that! Professor M. Fiendish, Esq. 05:36, 9 September 2009 (UTC)

The template list so far is incomplete. I'm not convinced it is practical to list them all happily, NOR what the best grouping should be. Prismatic uniform star polyhedra also ought to be included. Star pyramids as well! Tom Ruen (talk) 02:19, 15 September 2009 (UTC)

Classification

Mathworld lists 10 categories by vertex figures by Norman Johnson (mathematician): [1]. Tom Ruen (talk) 02:25, 15 September 2009 (UTC)

Johnson's classification looks favourable - and I note that the article List of uniform polyhedra by vertex figure uses this to a certain extent. If that is considered too fine-grained, then something a little coarser like along the following lines may do as well:

1. Uniform polyhedra with vertex on a rotational axis
2. Non-snub uniform polyhedra with vertex elsewhere on a reflection plane
3. Non-snub uniform polyhedra with vertex not on any reflection plane
4. Snub uniform polyhedra (those containing edges not bisected by a reflection plane)

Also, it would be nice to be able to navigate the non-convex uniform polyhedra within the context of all uniform polyhedra. While the convex ones form a coherent subset, the non-convex ones don't: there is nothing special per se about not being convex.Robert Stanforth (talk) 21:36, 18 September 2009 (UTC)

Hi Robert! Thanks for finishing the dual-star templates. Free free to try something here, Johnson's or whatever. I do think nonconvex articles could have both convex and nonconvex templates on the bottom. Anyway I'm promising myself to lay low for a while until I get some things done. Good luck! Tom Ruen (talk) 23:09, 18 September 2009 (UTC)

OH, I was inspired to move to { { Star polyhedron navigator } }. Also I should note that {{ Polyhedron navigator } } directs to convex forms. Tom Ruen (talk) 23:13, 18 September 2009 (UTC)

Uniform star-polyhedra

Nonconvex uniform polyhedra include (54 with skilling): Cubitruncated cuboctahedron Cubohemioctahedron Ditrigonal dodecadodecahedron Dodecadodecahedron Great cubicuboctahedron Great dirhombicosidodecahedron Great disnub dirhombidodecahedron Great ditrigonal dodecicosidodecahedron Great ditrigonal icosidodecahedron Great dodecahemicosahedron Great dodecahemidodecahedron Great dodecicosahedron Great dodecicosidodecahedron Great icosicosidodecahedron Great icosidodecahedron Great icosihemidodecahedron Great inverted snub icosidodecahedron Great retrosnub icosidodecahedron Great rhombidodecahedron Great rhombihexahedron Great snub dodecicosidodecahedron Great snub icosidodecahedron Great stellated truncated dodecahedron Great truncated cuboctahedron Great truncated icosidodecahedron Icosidodecadodecahedron Icositruncated dodecadodecahedron Inverted snub dodecadodecahedron Nonconvex great rhombicosidodecahedron Nonconvex great rhombicuboctahedron Octahemioctahedron Rhombicosahedron Rhombidodecadodecahedron Small cubicuboctahedron Small ditrigonal dodecicosidodecahedron Small ditrigonal icosidodecahedron Small dodecahemicosahedron Small dodecahemidodecahedron Small dodecicosahedron Small dodecicosidodecahedron Small icosicosidodecahedron Small icosihemidodecahedron Small retrosnub icosicosidodecahedron Small rhombidodecahedron Small rhombihexahedron Small snub icosicosidodecahedron Small stellated truncated dodecahedron Snub dodecadodecahedron Snub icosidodecadodecahedron Stellated truncated hexahedron Tetrahemihexahedron Truncated dodecadodecahedron Truncated great dodecahedron Truncated great icosahedron

Duals of uniform star-polyhedra

Duals of nonconvex uniform polyhedra include (54 with skilling's dual): Octahemioctacron Tetrahemihexacron Small hexacronic icositetrahedron Great hexacronic icositetrahedron Hexahemioctacron Tetradyakis hexahedron Great deltoidal icositetrahedron Small rhombihexacron Great triakis octahedron Great disdyakis dodecahedron Great rhombihexacron Small triambic icosahedron Small icosacronic hexecontahedron Small hexagonal hexecontahedron Small dodecacronic hexecontahedron Medial rhombic triacontahedron Small stellapentakis dodecahedron Medial deltoidal hexecontahedron Small rhombidodecacron Medial pentagonal hexecontahedron Medial triambic icosahedron Great ditrigonal dodecacronic hexecontahedron Small ditrigonal dodecacronic hexecontahedron Medial icosacronic hexecontahedron Tridyakis icosahedron Medial hexagonal hexecontahedron Great triambic icosahedron Great icosacronic hexecontahedron Small icosihemidodecacron Small dodecicosacron Small dodecahemidodecacron Great rhombic triacontahedron Great stellapentakis dodecahedron Rhombicosacron Great pentagonal hexecontahedron Great pentakis dodecahedron Medial disdyakis triacontahedron Medial inverted pentagonal hexecontahedron Great dodecacronic hexecontahedron Small dodecahemicosacron Great dodecicosacron Great hexagonal hexecontahedron Great dodecahemicosacron Great triakis icosahedron Great deltoidal hexecontahedron Great disdyakis triacontahedron Great inverted pentagonal hexecontahedron Great dodecahemidodecacron Great icosihemidodecacron Small hexagrammic hexecontahedron Great rhombidodecacron Great pentagrammic hexecontahedron Great dirhombicosidodecacron Great disnub dirhombidodecacron