Talk:Kepler-Poinsot polyhedron

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Mathematics rating: B Class Low Priority  Field: Geometry

The definition is unclear. The term "regular polyhedron" is not defined, and it is not clear whether different polygons may be used as faces. AxelBoldt 16:49, 2 Oct 2003 (UTC)


Why has this page been redirected to just "Kepler solid" rather than the correct name "Kepler-Poinsot solid"? I haven't heard anyone refer to these as just the Kepler solids. I think it should be changed, but it seems so odd that maybe there is a reason for it.

Also, I will change the term "lesser stellated dodecahedron" to "small stellated dodecahedron", which is really the only name by which this model is known today. And "greater dodecahedron" to just "great dodecahedron".

[edit] Complex polygons?

Where does the term complex polygon come from? I have done a fair bit of geometry, and the only 'complex polygons' I have come across are those where the polygonal boundary is in several separate parts, creating holes in the figure. I have never seen it used to describe selfintersecting polygons. Please either give a reference to this usage or change the wording. Steelpillow 22:34, 21 December 2006 (UTC)

I'll copy this comment to complex polygon, and change the link here to nonconvex polygon. Tom Ruen
Oops! I got ambitious. Hopefully better all around! Tom Ruen 00:22, 22 December 2006 (UTC)

[edit] History

Some of the history looks a little inaccurate:

Jamnitzer's 'stellated dodecahedron' does not have the face planes aligning from arm to arm - there is no evidence that he understands it as a dodecahedron. Nor is there any evidence that he understands this or his 'great dodecahedron' as being regular.

Uccello is sometimed credited with a marble tarsia, depicting a small stellated dodecahedron, in the floor of St. Mark's Basilica, Venice. But did he ever 'draw' one as the page says? Please either provide a reference or replace the comment with the tarsia (illustrated in Cromwell).

Poinsot used a definition of convexity, under which all these figures and their faces are convex (no concave vertices, y'see). This definition stuck for many decades. I am not sure when the modern usage arose, but is it worth noting the change?

I have a bit more to add when/if I get the time, eg Cauchy confirmed that Poinsot's list was complete, and Bertrand obtained them by facetting the Platonic solids. Steelpillow 20:38, 22 December 2006 (UTC)

Thanks for the look! I only sectioned the History information unchanged since I didn't take time to confirm or add to to it. Feel free to expand, or correct as you can. Tom Ruen 20:44, 22 December 2006 (UTC)
Done. Enjoy. Steelpillow 12:10, 24 December 2006 (UTC)