Talk:Johnson solid

1579:

and put them together. It can be hard to figure out what the "others" and the rotunda are all-around using just the picture. Just now I used them to make sure the triangular hebesphenorotunda's squares all had 3 triangles attached, which suggested it had triangular symmetry (the triplet of pentagons and their center triangle has the same plane of rotation as the hexagon), which I then confirmed at its article. The information you just added it reinforced by the nets. Some time ago, when I was generalizing these solids to 4D I mainly interpreted the nets, and didn't have this information about how the icosidodecahedron was related to the rotunda and so forth. Around this same time I also noticed the wedging theme in constructing the "others" by looking at their nets, because when I saw the pictures of the solids my eye didn't group the faces by those wedges, but in the Bilunabirotunda (

84: 74: 53: 176: 158: 299: 1107: 294: 1102: 1097: 349: 327: 322: 337: 332: 22: 1704: 948:. It's in the section of modified cupolas and rotundas, in that it can be viewed as a bicupola, but instead of the top being a polygon, it's a single edge, and the bottom is a square. You don't find a single one of these in normal cupolas/rotundas/pyramids though, because that would be simply a triangular prism. 2422:

The new format is just bad, I'm not even gonna lie. The old format made it so much more clear how they were all constructed, and also how they were related to each other. The new format just throws all of that out the window, and on top of it all, it removed the pictures too :( I don't understand why

1347:

To define the centre usefully, it would need to remain static under duality - that is, the centre of the dual must be the same point as the centre of the original. This ensures that when you dualise the dual, you get back to the original form. It turns out that for some figures this is really hard, I

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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

1578:

They are helpful. Looking again, they have different themes of construction, even if they're all the same type of modification, and some solids have more than one construction. I think the nets are helpful because they can give clues as to how the solids are similar to others and how to dissect them

1508:

Yes, that serves the original purposes I had used this article's classification for. If the solids are given in order in this table, then we don't need to group the solids in order here. Is there a reason for having the augmentation and diminishing subclasses as separate sections? Also, I found that

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ANy polyform with a platonic, archimedean, keplar-poinsot, uniform star polyhedral, or Johnson solid monoform. This includes the aformentioned antiprism stacks, polycubes, polytetrahedra, polytruncated octahedra, polyiamond prisms, polyhex prisms... and those are just the poly forms already mention

773:

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

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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

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This trisquare hexadecatrihedron has 16 triangular and 3 square faces, and looks somewhat like a cube embedded in an icosahedron (hence my informal name of 'cubicos'), . The squares are regular and the aggregate distortion in the lengths of the triangular edges is only about 0.1 in total (stress

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which generates all the Johnson solids. Previously I didn't have the patience to try uploading all 92 nets, but figured easier for me than generating all from scratch. By default Stella colors faces by symmetry positions. I only had patience to upload them by indexed names. Here they all are! Feel

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Biform star polyhedra with all regular faces. E.g. the cousins of the uniform star polyhedra with exactly two types of vertex. Then the triform, tetraform, etc. At least, my intuition is that you need to group these by number of unique vertex types to have any chance of listing them since I don't

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I'm not sure I follow. I hope the groupings here are helpful. Myself, I'm interested in showing similar non-Johnson solids as well, whether regular, semiregular, or having coplanar faces, so I started adding some of these. I added the bottom rows of the table on "augmented from polyhedra" to help

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Non-convex augmentations, including more than one type of face or augmenting adjacent faces that result in the biaugmented edges being non-convex. Just with cubes augment and para biaugmented are already coveredby the elongated square pyramid and elongated square bipyramid, but there's the meta

1665:

A new section on non-convex isomoprps has been added. I would suggest that these are not notable. Other classes of isomorph exist - convex and non-convex - but nobody has bothered to describe them, there is nothing notable about these ones either. A single fanboi web page does not constitute a

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This was not a good change. The classes made it easier to figure out how the solids were made and where the regular variations started and stopped, so that if you needed to do something for a set of the solids you could work out your process from choices in each class and extend it to the rest

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used the term in passing, and I believe it fits the bill of not asserting commonality, whilst being less dismissive than "Miscellaneous". This collection is the most interesting to me because the faces generate new angles, and as I was modeling with Geomag, this gave new model possibilities.

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Regular faced forms beyond the Johnson Solids and the Uniform star polyhedra strike me as being pretty deep waters that are far from well explored, or if they have, than much of the information is locked up in obscure places... and keep in mind, it took over two thousand years to go from the

2266:

mix stacks of prismatic forms. For every regular n-gon, there's a prismatic stack for every bit sequence where 0 and 1 represent prisms and anti-prisms... and then there's cupolae and pyramids to add to the mix... for example, you could take an elongated pentagonal copula and put a elongated

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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.

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The crossed cupolae have probably been described more widely: Johnson has terminology for them, so he might mention them somewhere. But yeah, most of these are just trivial and don't really need to be here, and after all they are just cut-and-paste operations. So I removed it again.

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it inconsistently uses "Johnson solid" as an adjective and then and a noun, i.e. sometimes prefixed with an article, sometimes not. It also omits articles for the named polyhedra. Overall it reads a little verbose and clunky. here's my proposed alternative:

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I think the value of multiple tables is that it easier to edit, and there were distinct groupings by named categories from Johnson's numbering, but it looks easy to delete the sections and table headers to remerge into a single table if you want to try.

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Archimedean solids to the Johnson Solids, the Archimedean solids where lost for much of that time, Johnson had to invent terminology to describe most of the Johnson Solids, and it's been less than 60 years since Johnson enumerated the Johnson Solids.

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biaugmented cube, two formas of triaugmented cube, two tetraagumented cubes, and the pentaaugmented and hexaaugmented cube. With 92 faces to pick from, the snub dodecahedron could potentially have hundreds or thousands of non-convex augmentations.

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Can anyone edit this article so that there's one large table of all 92 figures rather than several small tables?? This way, the table can be re-sorted by the number of faces each polyhedron has or any other appropriate way.

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is not Johnson solid because it is not convex, meaning whenever two points are interior, the connecting line may not. The last solid is not a Johnson solid because it is not convex, meaning every face is planar or the

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The terms "semicupola" (cuploids) and "sesquicupola" (cupolaic blend?) have been attributed to Johnson on some websites, so it's quite possible that he mentions them in his (still) forthcoming book, or somewhere else.

1352:, that all vertices be regular, i.e. having the same polygonal angle between adjacent edges. Not sure if that set of polyhedra would match the Johnson solids one-to-one, though: an interesting problem. — Cheers, 884:

All (it seems) of the individual Johnston solids pages were edited by 140.112.54.155 so that the table on each page listing the number of faces for the solid has entries like "3.5 triangles". They haven't

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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.

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column, listing the counts and types of vertices for each form. I made an automated tally once somewhere and I'll see if I can merge it in sometime - NOW that there's some screen width to play with.

1167:) 02:30, 11 October 2018 (UTC) Jim McNeill has demonstrated to my satisfaction that the referenced shape is indeed a near miss, having distortion mainly confined to the two isolated square faces. 2324: 1831: 1348:

seem to recall that even the "Stella" software author gave up on it and used a simpler algorithm. I think it would be fair to ignore centres and polar reciprocity but instead to require the dual

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think the term convex is well defined for self-intersecting forms... though I could be wrong and there's a finite set of regular faced, self-interesecting forms with all convex dihedral angles.

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The article says: A Johnson solid is a strictly convex polyhedron. As far as I know, a strictly convex polyhedron is a strictly convex set, and hence the edges can't contain straight lines.

1752:, Johnson solid failures due to adjacent coplanar edges, 78 forms, by Robert R Tupelo-Schneck. It says the listing was independently produced and proven complete in 2010 by A. V. Timofeenko. 565:

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" --

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I understand many readers or users would like to add the images for construction illustration purposes, but we do have guidelines about avoiding excessive exhibition images, discussed in

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as a single sortable table? (I definitely use the sort feature, by face counts, edge counts, or symmetry) Perhaps the list here should be simpler, without element counts, symmetry, etc?

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I like the brevity. We have an enthusiastic new editor who makes occasional lapses in English, likely including these missing articles; let's be patient and correct them as needed.

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If I'm understanding the question correctly, keeping all faces regular or regular star polygons while allowing different types of vertex, self-intersection, dihedral angles : -->

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in the information one needs to study these solids and learn their types. One can easily merge all the tables in a sandbox if one needs them ordered by a column of the table. ᛭

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What is the set of the polyhedrons whose faces are all regular polygons? (not need to be convex or uniform, and there is no requirement that each face must be the same polygon)

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I removed the "type" column from the tables in favor of a list of types at the beginning of each section. It took too much screen width and redundant with polyhedron names.

1515:, the tables will still sort the numbers inside the tag properly, so perhaps the beginnings of the sections in the original numeration can be labelled inside the table. ᛭ 532:

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?

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exp(7 i α) = (43+13i√2) / 27√3, which is in the first quadrant, implying that either 2π/7<α<5π/28 or 0<α<π/14; the latter is ruled out because tan(α) : -->

904:

They look like honest edits, although notation could be confusing, 3.5 meaning 3×5=15 triangles, while could look like 3+1/2. It looks like an attempt to group the

2485: 224: 1583:) for example first separating it along one of the hexagons crossing the midpoint, then grouping the faces of each piece into the front faces and back faces. ᛭ 457:

10th row sixth picture from the left you can see a view of elongated square gyrobicupola which is very distinct of rhombicuboctahedron. 19:45, 17 April 2010

1908:, there are 92 convex ones other than the regular polyhedrons and the semiregular polyhedrons, but what are the non-convex ones? (These would include the 4 623:

Actually, the Mathworld article was discussing all the simple convex regular-faced solids, including the simple Archimedean solids. There are 11 of these:

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I like it well enough, but making up our own words is against the rules; we need to find a term already in use in the field. For whatever it's worth,

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Not to my knowledge. I don't think they have even been enumerated in any reliable source. I'd probably call them "Johnson duals" for short. — Cheers,

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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

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Is there a name for the set of 92 polyhedra that are duals of the Johnson solids? Other than "duals of the Johnson solids"? (By analogy with the way

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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.

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free to "trace" or change arrangements in a complete set of SVG versions as your patience allows! I do think the symmetry coloring is worthy to use.

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One problem is that for a geometric dual – rather than a mere topological dual – you need a center. How do you choose centers for the 56 that lack

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it was even changed? like what's better abut this list? We already have a page that just lists them all out (AND HAS PICTURES ON TOP OF THAT!!!!!)

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show their construction, since some of the views, even transparent, are confusing to see easily. Anyway, I'd do more when I have some time.

200: 2480: 464: 2446:, containing a list of Johnson solids, and it is sufficient to give a table alongside the symmetry group and their metric properties. 2328: 2208: 1835: 2320:

This just confuses people. The stated definition prior to this ridiculous sentence is crystal clear, and we should leave it at that.

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with equilateral triangles is impossible uses the fact that 6 triangles add up to 360 degrees. But, here's a hard problem: prove the

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of triangles - there's 3 sets of 5 triangles in equivalent positions of symmetry. I don't keep a watch on all the individual pages.

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A good attempt. I've never tried, but the proof was the intention of Johnson's paper! There's another open-ended category called

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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.

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Johnson special.) Other possibilities are Johnson Unique, Johnson Peculiar, Johnson Disctinctive, Johnson Elemental, etc.

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confuse readers with all the things that it is not. Or any things that it is not. Like the sentence in the introduction:

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the "sporadics" 84-86 & 88-92, (87 is an augmented sporadic) They have no relation to platonics or archimedeans.

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There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex.

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How can we know that "Johnson has terminology for them" unless we know whether or not he mentioned them somewhere?

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that I've seen. Before I go fixing up 92 pages, is there any reason to believe this isn't vandalism? Thanks,

2150: 886: 2212: 2134: 1209: 979: 468: 2392: 2115:? (this is my question in this talk, what is the set of such polyhedrons, I know that this set include the 1198: 1126: 754:

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

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Now that there's enough nets for a whole section, anyone think we should incorporate them into the table?

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I have an old different tally on a test page - lists all reg/semireg/Johnson solids by vertex figure:

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for what may be the latest version. Here is where I am tracking progress. Bold numbers have images.

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as an experiment, copied from here, so this article could have a more compact summary by groupings?

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

21: 2182: 2146: 2142: 1640: 1588: 1520: 1437: 1278: 1243: 1213: 599:," and upon incautious consideration I agree with Knowledge's choice of terminology. —ajo, Apr 2005 407: 436:

I'm not sure that's possible. They don't call that the "pseudorhombicuboctahedron" for nothing.

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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Because the prisms and antiprisms are excluded, otherwise the list would be infinite in length.

73: 52: 1601:, although manually made nets might pick different arrangements for seeing the figures better. 1014:

In case the tables aren't clear enough for you: they are the elongated pentagonal birotundae. —

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And I'm sure there are forms that are regular faced but don't fit any of the above categories.

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

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Good point - the numbering was in Johnson's original paper. I have amended the article.

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I started reworking the first ones into topological groups. I'm not sure if this helps

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I need to know the name of the Johnson solid with 42 faces, 80 edges and 40 vertices.

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have. Did Johnson himself give the group a name? In fact, did he group them at all? —

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I hope someone knowledgeable about this subject will remove this idiotic sentence.

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p.s. I'm unsure if the nets are helpful here, so those rows might be removed.

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80 and 83 (parabidiminished & tridiminished rhombicosidodecahedra - ditto)

79: 2350:, is Johnson solid because it has the convexity property. The second solid, 2002: 1952:

Polyhedrons whose faces are all regular polygons (or regular star polygons)

1897: 196: 192: 1900:, but what are the non-convex ones? And for the polyhedrons with each face 1191:

It has 3 squares, 6+9 isosceles triangles, and 1 regular triangle. T.T OTL

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Have you proven that the faces are flat and regular? Models can flex. —

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p.s. on nets, the faces are colored by the symmetry, autogenerated by

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five squares eight triangles (eleven vertices) looks valid to me url=

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Okay, thanks. That's disturbing if MathWorld is totally wrong here.

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I added the nets to stub articles J47-92. Patience exhausted for now.

377: 2380:, as some of its diagonals lie outside the shape. The third presents 1114:

vertex figure: 1 (4,4,4), 3 (3,3,4,4), 3 (3,3,3,3,4), 5+5 (3,3,3,3,3)

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

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

2125:(Polyhedrons whose faces are not all regular polygons, such as the 1998: 1893: 1880:, and there are 9 non-convex regular polyhedrons, including the 4 806:

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

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Any connected subset of a honeycomb where all faces are regular.

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or which have a tiling of the plane or pace as a limiting case.

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Any views on the name "Sporadics" for this part of the series?

2346:"The following are three examples of solids. The first solid, 15: 1235:

This model is readily buildable with Polydrons. Jim McNeill

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You can search that for yourself - looks like at least two!

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on the list? Did I not understand the definitions enough? --

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Improve the description under the image with the 3 examples

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And the rest with Inkscape, now that I found out about it:

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which when added to the 17 simple Johnson solids, make 28.

2153:; and the polyhedrons with 180° dihedral angles, such as 1409:

Adding a "|-" before the headers seemed to do the trick!

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Incidentally, the Knowledge articles are using the term "

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Each face are the same polygon? (i.e. Identical faces?)

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Thanks, that's incredibly helpful to know about them! ᛭

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Can we like, go back to the old format with the tables?

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63 (tridiminished icosahedron - can't chop any further)

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Convex regular-faced polyhedra with conditional edges

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Convex regular-faced polyhedra with conditional edges

1238:keeps a catalog of near misses and lists this one. 187:, a collaborative effort to improve the coverage of 101:, a collaborative effort to improve the coverage of 1193:

How can prove or disprove no more Johnson solid? --

260:povray macros to generate images of as many of the 1450:Perhaps both are useful, grouped solids here, and 1186:I installed Great Stella software and test it but 604:I added a table of images at the end. Very useful. 229:This article has not yet received a rating on the 2368:Among these three polyhedra, only the first, the 2157:; and the non-connected polyhedrons, such as the 1892:, there are 13 convex ones other than the convex 1786:How would you define it? The excluded cases have 1708:(Just teasing, thanks for the revert). — Cheers, 1325:symmetry would also do, but there aren't any.) — 1057:hm, I guess I need to prove that α=atan(√2) : --> 1790:of zero, or having two faces in the same plane. 2222:The last row includes, for a start, a stack of 1845:Less well defined, as discussed in the section 734:http://mathworld.wolfram.com/JohnsonSolid.html 429:not a rhombicuboctahedron? —ajo, 21 April 2005 732:I computed the VEF counts by the table from: 8: 1242:map). Distortion (E=0.10, P=0 , A=18.3°). 1158:http://cs.sru.edu/~ddailey/tiling/hedra.html 494:I don't understand this comment. Clarify? 1876:, the convex regular polyhedrons are the 5 2267:pentagonal pyramid on its pentagonal face. 2079:uniform star prisms and uniform antiprisms 406:The picture is wrong - that's obviously a 152: 47: 2161:; and the degenerate polyhedras, such as 835:calls them "Complex Elementary Forms". — 781:calls them "Complex Elementary Forms". — 1950: 1112:faces: 16 triangles, 3 squares, total 19 867:User:Tomruen/Polyhedra_by_vertex_figures 1509:if you use <abbr title="heynow": --> 154: 49: 19: 2372:, is a Johnson solid. The second, the 2325:2601:200:C082:2EA0:2494:C097:5957:E04C 1832:2402:7500:586:91EF:6911:7EBA:959B:3B90 2486:Unknown-importance Polyhedra articles 2302:Completely irrelevant and distracting 1188:some triangles are not quite regular. 547:1-6 (pyramids, cupolae & rotunda) 455:http://peda.com/posters/img/poly4.gif 7: 1960:Uniform? (i.e. Identical vertices?) 1701: 858:I'd like to expand the table with a 739:Total faces by: F=F3+F4+F5+F6+F8+F10 181:This article is within the scope of 95:This article is within the scope of 683:The cube is excluded because ...? — 38:It is of interest to the following 2306:The definition of a Johnson solid 2169:; and the infinity forms, such as 1121:Discovered by me, David Park Jr.-- 944:It is on the list, under the name 316:I'm making some "home-made" nets: 14: 2476:Low-priority mathematics articles 2359:of two adjacent faces have 180°." 2270:Augmenting with prismatic stacks. 115:Knowledge:WikiProject Mathematics 1702: 1105: 1100: 1095: 1088:I DISCOVERED A NEW JOHNSON SOLID 758:A Name for the #84 - #92 group? 750:Computed edges by Euler: E=V+F-2 347: 335: 330: 325: 320: 297: 292: 174: 156: 118:Template:WikiProject Mathematics 82: 72: 51: 20: 209:Knowledge:WikiProject Polyhedra 135:This article has been rated as 2286:2603:6080:7001:8205:0:0:0:115C 1748:I found this interesting list 1512: 1061:cos(α) = 1/√3, sin(α) = √(2/3) 1042:is not a valid Johnson solid. 212:Template:WikiProject Polyhedra 1: 2370:elongated square gyrobicupola 2348:elongated square gyrobicupola 2255:Among other things, you have: 2191:truncated trihexagonal tiling 1840:03:53, 7 September 2020 (UTC) 1362:10:37, 27 February 2014 (UTC) 1335:07:09, 27 February 2014 (UTC) 845:09:33, 23 February 2009 (UTC) 826:14:56, 22 February 2009 (UTC) 416:No it is right. Look again. 402:Elongated square gyrobicupola 203:and see a list of open tasks. 109:and see a list of open tasks. 2471:B-Class mathematics articles 2083:nonconvex uniform polyhedras 1922:nonconvex uniform polyhedras 1859:06:17, 30 October 2020 (UTC) 1419:22:19, 13 October 2010 (UTC) 1403:21:48, 13 October 2010 (UTC) 1387:21:38, 13 October 2010 (UTC) 1212:, and some are listed here: 1177:12:02, 12 October 2018 (UTC) 1081:04:07, 19 October 2010 (UTC) 1052:22:06, 15 October 2010 (UTC) 918:01:06, 6 December 2007 (UTC) 899:00:45, 6 December 2007 (UTC) 617:19:48, 15 October 2005 (UTC) 441:01:18, 8 November 2006 (UTC) 2217:10:03, 29 August 2021 (UTC) 1847:duals of the Johnson solids 1826:, but what are the dual of 1645:10:23, 17 August 2013 (UTC) 1261:duals of the Johnson solids 1024:23:16, 29 August 2009 (UTC) 1008:22:48, 29 August 2009 (UTC) 993:11:10, 29 August 2009 (UTC) 928:Why isn't the tetraeder 4 F 875:07:56, 7 January 2007 (UTC) 715:14:14, 17 August 2010 (UTC) 693:16:50, 16 August 2010 (UTC) 675:03:07, 15 August 2010 (UTC) 652:truncated icosidodecahedron 274:User:AndrewKepert/polyhedra 2502: 2481:B-Class Polyhedra articles 2247:13:00, 5 August 2023 (UTC) 2117:augmented heptagonal prism 2058:Kepler–Poinsot polyhedrons 2001:, infinite convex uniform 1934:augmented heptagonal prism 1910:Kepler–Poinsot polyhedrons 1882:Kepler–Poinsot polyhedrons 1762:03:26, 14 April 2017 (UTC) 1734:12:38, 24 April 2014 (UTC) 1718:17:04, 22 April 2014 (UTC) 1696:14:09, 22 April 2014 (UTC) 1680:08:21, 19 April 2014 (UTC) 1611:02:13, 3 August 2013 (UTC) 1593:07:43, 1 August 2013 (UTC) 1562:06:14, 1 August 2013 (UTC) 1548:06:12, 1 August 2013 (UTC) 1525:06:06, 1 August 2013 (UTC) 1500:02:40, 1 August 2013 (UTC) 1482:00:15, 1 August 2013 (UTC) 1464:00:08, 1 August 2013 (UTC) 1225:17:31, 16 March 2011 (UTC) 1203:12:48, 16 March 2011 (UTC) 1146:07:24, 16 March 2011 (UTC) 1131:09:44, 15 March 2011 (UTC) 1093:Really! here are pictures! 1040:augmented heptagonal prism 515:19:25, Nov 21, 2004 (UTC) 266:User:AndrewKepert/poly.pov 231:project's importance scale 2456:11:14, 31 July 2024 (UTC) 2433:10:30, 31 July 2024 (UTC) 2412:23:06, 16 July 2024 (UTC) 2397:15:29, 16 July 2024 (UTC) 1800:15:12, 31 July 2017 (UTC) 1781:17:22, 30 July 2017 (UTC) 1442:23:22, 31 July 2013 (UTC) 1298:13:12, 6 April 2013 (UTC) 1283:04:10, 6 April 2013 (UTC) 1256:11:32, 10 July 2013 (UTC) 1030:Impossible Johnson solids 887:responded for explanation 801:09:04, 10 July 2006 (UTC) 540:05:52, 26 Jan 2005 (UTC) 490:09:13, 17 Nov 2004 (UTC) 393:18:11, 29 June 2008 (UTC) 378:23:46, 28 June 2008 (UTC) 228: 169: 134: 67: 46: 2342:Referring to this text: 2333:02:32, 8 July 2023 (UTC) 2294:20:08, 1 June 2024 (UTC) 2187:snub trihexagonal tiling 2135:near-miss Johnson solids 1997:infinite convex uniform 1581:File:Bilunabirotunda.png 1428:regularly. So there's a 1210:near-miss Johnson solids 968:19:15, 3 July 2008 (UTC) 940:11:14, 3 July 2008 (UTC) 851:Table changes ongoing... 786:23:42, 8 July 2006 (UTC) 584:22:15, 27 Jan 2005 (UTC) 569:07:58, 27 Jan 2005 (UTC) 544:Off the top of my head: 528:"simple" Johnson solids? 523:00:29, 22 Nov 2004 (UTC) 502:05:54, 26 Jan 2005 (UTC) 313:00:27, 5 Nov 2004 (UTC) 141:project's priority scale 2201:; are not in this set) 1930:uniform star antiprisms 1890:semiregular polyhedrons 1169:David.daileyatsrudotedu 1161:David.daileyatsrudotedu 1064:exp(i α) = (1+i√2) / √3 643:truncated cuboctahedron 420:03:47, 9 Nov 2004 (UTC) 280:Images of the flat kind 98:WikiProject Mathematics 2444:List of Johnson solids 2237:is plural, darn it.) — 2229:-antiprisms joined at 2100:non-convex deltahedras 1806:Dual of Johnson solids 1470:List of Johnson solids 1452:List of Johnson solids 646:truncated dodecahedron 252:I have been modifying 28:This article is rated 2442:. We have an article 2308:absolutely should not 2199:apeirogonal antiprism 1231:Previously discovered 649:truncated icosahedron 634:truncated tetrahedron 184:WikiProject Polyhedra 1918:stellated octahedron 1872:does not need to be 1372:Organizing the table 860:vertex configuration 640:truncated octahedron 359:Complete set of nets 121:mathematics articles 2183:trihexagonal tiling 2147:Szilassi polyhedron 2143:rhombic icosahedron 1953: 1926:uniform star prisms 408:rhombicuboctahedron 2151:Császár polyhedron 2007:Archimedean solids 1951: 1938:pentagrammic prism 1870:Regular polyhedron 1818:, and the dual of 1812:Archimedean solids 1271:Archimedean solids 1152:another near miss? 215:Polyhedra articles 90:Mathematics portal 34:content assessment 2195:apeirogonal prism 2171:triangular tiling 2131:hexagonal pyramid 2123: 2122: 2062:regular compounds 1914:regular compounds 1886:regular compounds 1599:Stella (software) 1269:are duals of the 1036:hexagonal pyramid 970: 954:comment added by 811:User:AndrewKepert 658:snub dodecahedron 463:comment added by 453:When you look at 365:Stella (software) 245: 244: 241: 240: 237: 236: 151: 150: 147: 146: 2493: 2374:stella octangula 2352:stella octangula 2179:hexagonal tiling 1954: 1902:regular polygons 1707: 1706: 1705: 1514: 1430:Pareto principle 1109: 1104: 1099: 1071:What do I win? — 949: 880:Suspicious edits 770: 769: 765: 488:Charles Matthews 472: 351: 339: 334: 329: 324: 301: 296: 217: 216: 213: 210: 207: 178: 171: 170: 160: 153: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 2501: 2500: 2496: 2495: 2494: 2492: 2491: 2490: 2461: 2460: 2420: 2357:dihedral angles 2340: 2304: 1982:Platonic solids 1946:toroidal prisms 1896:and the convex 1878:Platonic solids 1867: 1824:Platonic solids 1820:Platonic solids 1808: 1788:dihedral angles 1769: 1767:Strictly convex 1746: 1703: 1668:reliable source 1663: 1510:2</abbr: --> 1374: 1263: 1233: 1184: 1154: 1119: 1091: 1032: 976: 946:Gyrobifastigium 934:Saippuakauppias 931: 926: 882: 853: 771: 767: 763: 761: 760: 727: 530: 509: 507:Johnson numbers 483: 458: 404: 361: 282: 264:as I can. See 250: 214: 211: 208: 205: 204: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 2499: 2497: 2489: 2488: 2483: 2478: 2473: 2463: 2462: 2459: 2458: 2419: 2416: 2415: 2414: 2386: 2385: 2361: 2360: 2339: 2336: 2303: 2300: 2299: 2298: 2297: 2296: 2281: 2278: 2274: 2271: 2268: 2264: 2260: 2256: 2253: 2159:crossed prisms 2139:parallelepiped 2127:Catalan solids 2121: 2120: 2113: 2110: 2107: 2103: 2102: 2096: 2093: 2090: 2086: 2085: 2075: 2072: 2069: 2065: 2064: 2054: 2051: 2048: 2044: 2043: 2041:Johnson solids 2037: 2034: 2031: 2027: 2026: 2020: 2017: 2014: 2010: 2009: 1995: 1992: 1989: 1985: 1984: 1978: 1975: 1972: 1968: 1967: 1964: 1961: 1958: 1888:, and for the 1866: 1863: 1862: 1861: 1828:Johnson solids 1816:Catalan solids 1807: 1804: 1803: 1802: 1768: 1765: 1745: 1742: 1741: 1740: 1739: 1738: 1737: 1736: 1662: 1659: 1658: 1657: 1656: 1655: 1654: 1653: 1652: 1651: 1650: 1649: 1648: 1647: 1622: 1621: 1620: 1619: 1618: 1617: 1616: 1615: 1614: 1613: 1569: 1568: 1567: 1566: 1565: 1564: 1550: 1530: 1529: 1528: 1527: 1503: 1502: 1484: 1466: 1447: 1446: 1445: 1444: 1422: 1421: 1406: 1405: 1373: 1370: 1369: 1368: 1367: 1366: 1365: 1364: 1340: 1339: 1338: 1337: 1301: 1300: 1267:Catalan solids 1262: 1259: 1232: 1229: 1228: 1227: 1192: 1190: 1183: 1180: 1153: 1150: 1149: 1148: 1120: 1117: 1115: 1113: 1094: 1090: 1085: 1084: 1083: 1069: 1065: 1062: 1059: 1031: 1028: 1027: 1026: 1011: 1010: 975: 972: 929: 925: 922: 921: 920: 881: 878: 852: 849: 848: 847: 804: 803: 789: 788: 759: 756: 752: 751: 748: 747: 746: 740: 726: 723: 722: 721: 720: 719: 718: 717: 698: 697: 696: 695: 678: 677: 664: 661: 659: 656: 653: 650: 647: 644: 641: 638: 637:truncated cube 635: 632: 629: 626: 624: 620: 619: 611: 608: 605: 601: 600: 595:" instead of " 588: 587: 586: 585: 571: 570: 563: 559: 558: 557: 554: 551: 548: 529: 526: 525: 524: 508: 505: 504: 503: 482: 479: 478: 477: 476: 475: 474: 473: 446: 445: 444: 443: 431: 430: 422: 421: 403: 400: 398: 396: 395: 360: 357: 353: 352: 341: 340: 303: 302: 281: 278: 262:Johnson solids 258:image:Poly.pov 249: 246: 243: 242: 239: 238: 235: 234: 227: 221: 220: 218: 201:the discussion 179: 167: 166: 161: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 2498: 2487: 2484: 2482: 2479: 2477: 2474: 2472: 2469: 2468: 2466: 2457: 2453: 2449: 2445: 2441: 2437: 2436: 2435: 2434: 2430: 2426: 2417: 2413: 2409: 2405: 2401: 2400: 2399: 2398: 2394: 2390: 2383: 2379: 2375: 2371: 2367: 2366: 2365: 2358: 2353: 2349: 2345: 2344: 2343: 2337: 2335: 2334: 2330: 2326: 2321: 2318: 2316: 2311: 2309: 2301: 2295: 2291: 2287: 2282: 2279: 2275: 2272: 2269: 2265: 2261: 2257: 2254: 2250: 2249: 2248: 2244: 2240: 2236: 2232: 2228: 2225: 2221: 2220: 2219: 2218: 2214: 2210: 2206: 2202: 2200: 2196: 2192: 2188: 2184: 2180: 2176: 2175:square tiling 2172: 2168: 2164: 2160: 2156: 2152: 2148: 2144: 2140: 2136: 2132: 2128: 2118: 2114: 2111: 2108: 2105: 2104: 2101: 2097: 2094: 2091: 2088: 2087: 2084: 2080: 2076: 2073: 2070: 2067: 2066: 2063: 2059: 2055: 2052: 2049: 2046: 2045: 2042: 2038: 2035: 2032: 2029: 2028: 2025: 2021: 2018: 2015: 2012: 2011: 2008: 2004: 2000: 1996: 1993: 1990: 1987: 1986: 1983: 1979: 1976: 1973: 1970: 1969: 1965: 1962: 1959: 1956: 1955: 1949: 1947: 1943: 1939: 1935: 1931: 1927: 1923: 1919: 1915: 1911: 1907: 1906:star polygons 1903: 1899: 1895: 1891: 1887: 1883: 1879: 1875: 1871: 1864: 1860: 1856: 1852: 1848: 1844: 1843: 1842: 1841: 1837: 1833: 1829: 1825: 1821: 1817: 1813: 1805: 1801: 1797: 1793: 1789: 1785: 1784: 1783: 1782: 1778: 1774: 1766: 1764: 1763: 1759: 1755: 1751: 1743: 1735: 1731: 1727: 1722: 1721: 1719: 1715: 1711: 1699: 1698: 1697: 1693: 1689: 1684: 1683: 1682: 1681: 1677: 1673: 1669: 1660: 1646: 1642: 1638: 1634: 1633: 1632: 1631: 1630: 1629: 1628: 1627: 1626: 1625: 1624: 1623: 1612: 1608: 1604: 1600: 1596: 1595: 1594: 1590: 1586: 1582: 1577: 1576: 1575: 1574: 1573: 1572: 1571: 1570: 1563: 1559: 1555: 1551: 1549: 1545: 1541: 1536: 1535: 1534: 1533: 1532: 1531: 1526: 1522: 1518: 1507: 1506: 1505: 1504: 1501: 1497: 1493: 1490:'s purpose. 1489: 1485: 1483: 1479: 1475: 1471: 1467: 1465: 1461: 1457: 1453: 1449: 1448: 1443: 1439: 1435: 1431: 1426: 1425: 1424: 1423: 1420: 1416: 1412: 1408: 1407: 1404: 1400: 1396: 1391: 1390: 1389: 1388: 1384: 1380: 1371: 1363: 1359: 1355: 1351: 1346: 1345: 1344: 1343: 1342: 1341: 1336: 1332: 1328: 1324: 1320: 1316: 1312: 1310: 1305: 1304: 1303: 1302: 1299: 1295: 1291: 1287: 1286: 1285: 1284: 1280: 1276: 1272: 1268: 1260: 1258: 1257: 1253: 1249: 1245: 1244: 1239: 1237: 1230: 1226: 1222: 1218: 1214: 1211: 1207: 1206: 1205: 1204: 1200: 1196: 1189: 1181: 1179: 1178: 1174: 1170: 1166: 1162: 1159: 1151: 1147: 1143: 1139: 1135: 1134: 1133: 1132: 1128: 1124: 1110: 1108: 1103: 1098: 1089: 1086: 1082: 1078: 1074: 1070: 1066: 1063: 1060: 1056: 1055: 1054: 1053: 1049: 1045: 1041: 1037: 1029: 1025: 1021: 1017: 1013: 1012: 1009: 1005: 1001: 997: 996: 995: 994: 991: 987: 984: 981: 973: 971: 969: 965: 961: 957: 953: 947: 942: 941: 938: 935: 923: 919: 915: 911: 907: 903: 902: 901: 900: 896: 892: 888: 879: 877: 876: 873: 869: 868: 863: 861: 856: 850: 846: 842: 838: 834: 830: 829: 828: 827: 823: 819: 815: 812: 807: 802: 799: 796: 791: 790: 787: 784: 780: 777: 776: 775: 766: 757: 755: 749: 744: 743: 741: 738: 737: 736: 735: 730: 724: 716: 712: 708: 704: 703: 702: 701: 700: 699: 694: 690: 686: 682: 681: 680: 679: 676: 672: 668: 665: 662: 660: 657: 654: 651: 648: 645: 642: 639: 636: 633: 630: 627: 625: 622: 621: 618: 615: 612: 609: 606: 603: 602: 598: 594: 590: 589: 583: 579: 575: 574: 573: 572: 568: 567:Andrew Kepert 564: 560: 555: 552: 549: 546: 545: 543: 542: 541: 539: 535: 527: 522: 521:Andrew Kepert 518: 517: 516: 514: 506: 501: 497: 493: 492: 491: 489: 480: 470: 466: 465:74.125.121.33 462: 456: 452: 451: 450: 449: 448: 447: 442: 439: 435: 434: 433: 432: 428: 424: 423: 419: 418:Andrew Kepert 415: 414: 413: 412: 409: 401: 399: 394: 390: 386: 382: 381: 380: 379: 375: 371: 366: 358: 356: 350: 346: 345: 344: 338: 333: 328: 323: 319: 318: 317: 314: 312: 310: 309: 300: 295: 291: 290: 289: 287: 279: 277: 276: 275: 272:Relocated to 269: 267: 263: 259: 255: 247: 232: 226: 223: 222: 219: 202: 198: 194: 190: 186: 185: 180: 177: 173: 172: 168: 165: 162: 159: 155: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 2421: 2387: 2362: 2341: 2322: 2319: 2314: 2312: 2307: 2305: 2234: 2230: 2226: 2223: 2209:36.234.85.41 2203: 2124: 1868: 1846: 1810:The dual of 1809: 1770: 1747: 1726:Double sharp 1688:Double sharp 1670:. — Cheers, 1664: 1375: 1349: 1322: 1318: 1314: 1308: 1264: 1246: 1240: 1234: 1187: 1185: 1155: 1111: 1092: 1087: 1034:Proving the 1033: 977: 943: 927: 905: 883: 870: 864: 857: 854: 816: 808: 805: 779:Steven Dutch 772: 753: 731: 728: 631:dodecahedron 531: 510: 484: 438:RobertAustin 426: 405: 397: 362: 354: 342: 315: 307: 304: 283: 271: 270: 251: 195:, and other 182: 137:Low-priority 136: 96: 62:Low‑priority 40:WikiProjects 2389:Introscopia 2204:Reference: 2024:deltahedras 1942:deltahedras 1904:or regular 1710:Steelpillow 1672:Steelpillow 1379:Georgia guy 1354:Steelpillow 1290:Steelpillow 1248:Karl Horton 1195:David P.Jr. 1123:David P.Jr. 1044:Georgia guy 950:—Preceding 891:Fractalchez 818:Karl Horton 628:tetrahedron 459:—Preceding 410:. Compare: 286:makepolys.c 112:Mathematics 103:mathematics 59:Mathematics 2465:Categories 2448:Dedhert.Jr 2425:Digital542 2233:-faces. ( 2167:hosohedron 2003:antiprisms 1898:antiprisms 1884:and the 5 1116:symmetry:C 593:elementary 513:Factitious 2376:, is not 2098:infinite 2077:infinite 2022:8 convex 1920:, the 53 1822:are also 1661:Isomorphs 1637:LokiClock 1585:LokiClock 1517:LokiClock 1488:LokiClock 1434:LokiClock 1350:condition 1275:DavidCary 1068:tan(π/4). 980:Professor 924:Tetraeder 833:this page 725:NEW TABLE 707:Mongo62aa 667:Mongo62aa 655:snub cube 427:obviously 206:Polyhedra 197:polytopes 193:polyhedra 164:Polyhedra 2404:—Tamfang 2382:coplanar 2163:dihedron 2155:this one 1957:Convex? 1948:, etc.) 1912:, the 5 1849:above. — 1792:Tom Ruen 1754:Tom Ruen 1603:Tom Ruen 1554:Tom Ruen 1540:Tom Ruen 1492:Tom Ruen 1474:Tom Ruen 1468:I added 1456:Tom Ruen 1411:Tom Ruen 1395:Tom Ruen 1311:symmetry 1217:Tom Ruen 1000:Tom Ruen 986:Fiendish 964:contribs 956:Timeroot 952:unsigned 910:Tom Ruen 872:Tom Ruen 795:sjorford 614:Tom Ruen 578:dbenbenn 534:dbenbenn 496:dbenbenn 481:The list 461:unsigned 385:Tom Ruen 370:Tom Ruen 254:user:Cyp 189:polygons 2239:Tamfang 1851:Tamfang 1327:Tamfang 1138:Tamfang 1073:Tamfang 1016:Tamfang 974:Urgent! 837:Tamfang 783:Tamfang 685:Tamfang 363:I have 139:on the 30:B-class 2440:WT:WPM 2384:faces. 2378:convex 2235:–hedra 2149:, the 2145:, the 2141:, the 2137:, the 2133:, the 2129:, the 2112:False 2109:False 2106:False 2092:False 2089:False 2074:False 2068:False 2047:False 2036:False 2033:False 2016:False 1999:prisms 1994:False 1966:Class 1944:, the 1940:, the 1936:, the 1932:, the 1928:, the 1924:, the 1916:, the 1894:prisms 1874:convex 1773:Madyno 1182:failed 762:": --> 597:simple 248:Images 36:scale. 2095:True 2081:, 53 2071:True 2053:True 2050:True 2030:True 2019:True 2013:True 2005:, 13 1991:True 1988:True 1977:True 1974:True 1971:True 1273:). -- 1058:2π/7. 906:types 306:Κσυπ 2452:talk 2429:talk 2408:talk 2393:talk 2329:talk 2290:talk 2243:talk 2213:talk 2165:and 2060:, 5 1855:talk 1836:talk 1814:are 1796:talk 1777:talk 1758:talk 1730:talk 1714:Talk 1692:talk 1676:Talk 1641:talk 1607:talk 1589:talk 1558:talk 1544:talk 1521:talk 1496:talk 1478:talk 1460:talk 1438:talk 1415:talk 1399:talk 1383:talk 1358:Talk 1331:talk 1294:Talk 1279:talk 1252:talk 1221:talk 1199:talk 1173:talk 1165:talk 1142:talk 1127:talk 1077:talk 1048:talk 1020:talk 1004:talk 990:Esq. 960:talk 914:talk 895:talk 841:talk 822:talk 764:edit 711:talk 689:talk 671:talk 582:talk 538:talk 500:talk 469:talk 389:talk 374:talk 2039:92 1321:or 1317:or 1313:? 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