Talk:Johnson solid

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Contents 1 Images 2 Images of the flat kind 3 Elongated square gyrobicupola 4 The list 5 Johnson numbers 6 "simple" Johnson solids? 7 NEW TABLE 8 A Name for the #84 - #92 group?

[edit] Images

I have been modifying user:Cyp's image:Poly.pov povray macros to generate images of as many of the Johnson solids as I can. See User:AndrewKepert/poly.pov for what may be the latest version. Here is where I am tracking progress. Bold numbers have images.

Relocated to User:AndrewKepert/polyhedra

[edit] Images of the flat kind

Doesn't do 3d, and only knows 2 Johnson solids (so far), but here's makepolys.c.

Κσυπ Cyp   00:27, 5 Nov 2004 (UTC)

[edit] Elongated square gyrobicupola

The picture is wrong - that's obviously a rhombicuboctahedron. Compare: [1]

• No it is right. Look again. Andrew Kepert 03:47, 9 Nov 2004 (UTC)

It's definitely an image of the right polyhedron, but it's taken from an unflattering angle. Could someone POVRay up an image that is at first glance obviously not a rhombicuboctahedron? —ajo, 21 April 2005

I'm not sure that's possible. They don't call that the "pseudorhombicuboctahedron" for nothing. RobertAustin 01:18, 8 November 2006 (UTC)

[edit] The list

Usually it would be called good practice to make a list such as that in this article stand-alone. Not something to insist on, perhaps, in this case; but it is something to think about, in the way of writing the article so that it doesn't 'wrap' round having the list there in the current way. Charles Matthews 09:13, 17 Nov 2004 (UTC)

I don't understand this comment. Clarify? dbenbenn | talk 05:54, 26 Jan 2005 (UTC)

[edit] Johnson numbers

Is the numbering of the Johnson solids arbitrary? If not, how are the Johnson numbers determined? I think this should be mentioned in the article. Factitious 19:25, Nov 21, 2004 (UTC)

Good point - the numbering was in Johnson's original paper. I have amended the article. Andrew Kepert 00:29, 22 Nov 2004 (UTC)

[edit] "simple" Johnson solids?

28 of the Johnson solids are "simple". Non-simple means you can cut the solid with a plane into two other regular-faced solids. But it isn't clear which ones. Anyone? dbenbenn | talk 05:52, 26 Jan 2005 (UTC)

Off the top of my head:

• 1-6 (pyramids, cupolae & rotunda)
• 63 (tridiminished icosahedron - can't chop any further)
• 80 and 83 (parabidiminished & tridiminished rhombicosidodecahedra - ditto)
• the "sporadics" 84-86 & 88-92, (87 is an augmented sporadic) They have no relation to platonics or archimedeans.

which makes 6+1+2+8 = 17. There are other components from the platonic, archimedean, prisms and antiprisms that could arguably considered as needed for a building any of the J solids, but these are not "of the J solids". I think I have all or most of the list here, given your defn - well short of 28.

Where did you get 28? ... ah I see it in the mathworld article. Google throws up no other ref to "simple johnson solid". I suspect Mathworld is wrong, probably in the defn of "simple" --Andrew Kepert 07:58, 27 Jan 2005 (UTC)

Okay, thanks. That's disturbing if MathWorld is totally wrong here. dbenbenn | talk 22:15, 27 Jan 2005 (UTC)

Incidentally, the Wikipedia articles are using the term "elementary" instead of "simple," and upon incautious consideration I agree with Wikipedia's choice of terminology. —ajo, Apr 2005

I added a table of images at the end. Very useful.

Probably the list should be moved to "List of Johnson solids", and then this article can be shorter.

I'd like more statistics on these solids - Vertex, Edge, Face counts (and types of faces), Symmetry group. (I don't have this information) When this is available, making a data table would be more useful.

Tom Ruen 19:48, 15 October 2005 (UTC)

[edit] NEW TABLE

I added a new table with columns: Name, image, Type, Vertices, Edges, Faces, (Face counts by type 3,4,5,6,8,10), and Symmetry.

I computed the VEF counts by the table from: http://mathworld.wolfram.com/JohnsonSolid.html

Total faces by: F=F3+F4+F5+F6+F8+F10

Computed total internal angle_sum=180*(F3+2*F4+3*F5+4*F6+6*F8+8*F10)

Used angle defect sum to compute vertices: V=chi+angle_sum/360 (chi=2 for topological spheres)

Computed edges by Euler: E=V+F-2

The results should be correct, but may not be correctly matched by names if the indices were inconsistent!

[edit] A Name for the #84 - #92 group?

The series #84 - #92 are not derived from cut-and-paste of Platonics, Archimedians, and prisms. I put forth a trial name in the table: Johnson Special solids, after fiddling with a thesaurus for a while, thinking that they deserved better than "Miscellaneous". (One of them is actually an augmented Johnson special.) Other possibilities are Johnson Unique, Johnson Peculiar, Johnson Disctinctive, Johnson Elemental, etc.

Steven Dutch calls them "Complex Elementary Forms". —Tamfang 23:42, 8 July 2006 (UTC)

They're not really a set though, are they? As far as I can see, only the sphenocoronas form a set, and all the others are one-of-a-kind shapes. I think some sort of generic name like "Miscellaneous" or "Other" is the best way to describe them. "Special" indicates some sort of status they don't really have. Did Johnson himself give the group a name? In fact, did he group them at all? — sjorford++ 09:04, 10 July 2006 (UTC)

Very well, I will revert it back to Miscellaneous as I found it.