Talk:Dodecahedron

message: I don't think Dodecaeder should be merged with dodecahedron.  I think
there should be two separate pages: one dealing with  the Platonic solid and one dealing with the weird antique.  Merge request deleted and "see also" added.
Robinh 21:00, 26 May 2005 (UTC)
replies: text: There are some pictures here; it's a cuboctahedron.  Should probably delete the trivia item. --Matt McIrvin 04:11, 31 July 2005 (UTC)
thread_title: Untitled

message: Can someone explain or update the canonical coordiantes:
"Canonical coordinates for the vertices of a dodecahedron centered at the origin are {(0,±1/φ,±φ), (±1/φ,±φ,0), (±φ,0,±1/φ), (±1,±1,±1)}, where φ = (1+√5)/2 is the golden mean."
if there are 20 vertices, then why are there not 20 coordinate sets (x, y, z)? Zalamandor 23:23, 8 December 2005 (UTC)
thread_title:  Dodecahedron Canonical coordinates 

message: I replace stat table with template version, which uses tricky nested templates as a "database" which allows the same data to be reformatted into multiple locations and formats. See here for more details: User:Tomruen/polyhedron_db_testing
: Tom Ruen 00:55, 4 March 2006 (UTC)
thread_title:  New stat table 

message: I removed this long unsupported statement under "uses":
* If each edge of a dodecahedron is a one-ohm resistor, the resistance between adjacent vertices is 19/30 ohm, and that between opposite vertices is 7/6 ohm. 
I stumbled upon this paper , but couldn't clearly confirm or contradict the uncited statement above. So here it is if anyone cares! Tom Ruen 02:37, 29 September 2006 (UTC)
replies: text: It's right there in Table I (page 643). It also gives the resistances between vertices which are neither adjacent nor opposite. —Keenan Pepper 06:01, 30 September 2006 (UTC)
thread_title:  Electrical resistance 

message: The dihedral angle formula is wrong in the frame on the side of the article and I could not find how to modify this frame. (Unsigned comment)
:The correct formula is \pi - 2\psi where \psi is defined by:
::\cos(\psi) = \csc(\pi/5) \cos(\pi/3) = \cos(\pi/3)/\sin(\pi/5)
:(This is from Coxeter's Regular Polytopes.)—Tetracube 17:54, 13 November 2006 (UTC)
thread_title:  Dihedral angle in the frame 

message: I renamed the "Uses" section because only one of the three facts listed can be considered an "use" of a Dodecahedron (the die).
I'm not sure that "Trivia" is a good name, another possibility is "curious facts".
Ossido 16:29, 30 December 2006 (UTC)
thread_title:  Uses Vs Trivia 

message: * The ones missing are the octahedral pentagonal dodecahedron, the tetrahedral pentagonal dodecahedron, and the trapezoidal dodecahedron.
* If you look up "Isohedron" on Mathworld, you can see a rotating models of each of them.
* As a side note, I would love to know if the pyritohedron is the same thing as either the octahedral or tetrahedral pentagonal dodecahedron.  —Preceding unsigned comment added by 63.72.235.4 (talk) 15:15, 10 February 2009 (UTC)
replies: text: (I took the liberty of adding the relevant link.)  It's hard to tell from the small picture, but yes, I think the octahedral pentagonal dodecahedron is the "pyritohedron" (a name I dislike: it's the whole body, not the faces, that resembles a pyrite crystal). It has Th symmetry. —Tamfang (talk) 17:27, 12 February 2009 (UTC)
thread_title:  There are a few face-transitive (with congruent but irregular faces) dodecahedrons missing from the list 

message: I removed the following text from the article, added by an IP, because it wasn't added in the right place and was uncited; I wasn't sure what to do with it:
:Skeletal Platonic Solids
:If  the regular poyhedra are considered as skeletal 3-dimensional figures with flexible vertices and unidimensional edges, two of them. the hexadron(cube) and the dodecahedron exhibit properties different from the other three in that they can be folded or collapsed; The hexahedron first into a double square then a line. and the dodecahedron into a triangle. This can be demonstrated by constructing them out of drinking straws and twistable inserts
Somebody please verify this, find a citation, and integrate it into the article. Thanks.—Tetracube (talk) 03:18, 30 March 2009 (UTC)
replies: text: It's correct that the hexahedron, or cube, and the dodecahedron, if you make them out of drinking straws and twistable inserts, can be collapsed, but what they collapse into is wrong. --Professor M. Fiendish 12:07, 22 August 2009 (UTC)
thread_title:  Skeletal Platonic solids 

message: The formula "2 acos(36)" seems to make no sense. Should it be 2 acos(36°), or is it completely wrong? -- 05:42, 19 October 2009 (UTC)
replies: text: The argument to acos must be a value between -1 and 1, otherwise it is undefined. I don't know where this formula came from, but it looks suspiciously wrong.—Tetracube (talk) 17:03, 19 October 2009 (UTC)

text: If it makes any sense, it should be 2cos(36°). Tom Ruen (talk) 19:29, 19 October 2009 (UTC)

text: It is a pretty trivial claim, more about a pentagon than as a polyhedron, unclear value. Ugh, the more I look the more the whole article seems a largely unorganized collection of unrelated facts. Tom Ruen (talk) 00:02, 20 October 2009 (UTC)
thread_title:  "2 acos(36)" 

message: Is it really bigger than an icosahedron when made to fit in a sphere? References/Math? Simanos (talk) 15:32, 1 March 2010 (UTC)
replies: text: Using the numeric values given for volume and circumradius in the respective articles, I get the ratios 0.6649 for the dodecahedron, 0.6055 for the icosahedron.  I tried it with the algebraic formulae but made a booboo somewhere (getting a dodec >3 times as big as its circumsphere). —Tamfang (talk) 20:20, 2 March 2010 (UTC)
thread_title: filling a sphere

message: According to Carl Sagan during his TV series Cosmos - Knowledge of the Dodecahedron was kept hidden and suppressed by the Pythagoreans who discovered it. Should this be added into the history section on the shape? Omega2064 (talk) 19:03, 4 July 2010 (UTC)
replies: text: If you can cite a reliable source for it, yes.—Tetracube (talk) 14:43, 7 July 2010 (UTC)
thread_title: Regarding the supression of the Dodecahedron?

message: If I have done my math right, the maximum field of view occupied by a face as seen from the center of the dodecahedron is 2*acos[1.1135/1.40126], or just under 75.76 degrees. This might be of interest in selecting the field of view needed for the lens of an omnidirectional camera setup, for instance. With a typical aspect-ratio rectangular sensor such a 35mm film only the angle between a vertex and the center of the opposite side needs to fit on the shorter side of the sensor (24mm for 35mm film), so the calculation of the longest 35mm-equivalent lens that can fit a whole pentagon in the frame from the center of a dodecahedron is 1/(tan[(acos[1.1135/1.40126] + acos[1.1135/1.30902] )/2 ] /12) = 17.43mm max lens length. (the 12 in the calculation is = 1/2 the film width) 
Some stats useful for doing calculations for other sensors: if the height is 24mm as stated before, then the side of the pentagon is just under 15.6mm, the width (penagon's diagonal) is under 25.24mm, and the diameter of the circumscribing circle is less than 26.54mm. A square sensor should be able to use a longer lens.Enon (talk) 23:48, 24 February 2011 (UTC)
thread_title:  Field of view of 

message: To draw a dodecahedron myself, I had to reverse the Golden Ratio with its inverse in the Cartesian coordinates, or change the rotation of the indices.  As I don't believe I'm having this problem drawing other things, I'd appreciate it if someone would check what's here.  I'm using a right-handed coordinate system.  Short of that, I wasn't clear on what tag to use, as I couldn't find a section-limited expert needed tag.  So if someone improves on how I tagged this, that's great too.  Thanks!  Marc W. Abel (talk) 01:40, 3 May 2011 (UTC)
replies: text: The coordinates are on the MathWorld page, and I have no reason to doubt them. Left-handed coordinates would make no difference. You can see the regular dodecahedron with the 8 vertices of the cube, plus 2 vertices above each of the square faces, forming wedges over each square. The side triangles of the wedges merge with side trapezoids as regular pentagons, as seen in the related irregular Pyritohedron#Geometric_freedom. Tom Ruen (talk) 05:26, 3 May 2011 (UTC)

text: What are you using to "draw"? —Tamfang (talk) 05:59, 3 May 2011 (UTC)
replies: text: At a guess you might be drawing only one side of you polygons, whether polygon is displayed depends on which face is pointing towards the viewer, if its the notional "front" face then the polygon is displayed, if not the polygon is not displayed, see backface culling. Changing the order of the vertices changes the notion of which is the front face and hence the visibility.--Salix (talk): 14:40, 3 May 2011 (UTC)
thread_title:  Are these left-handed Cartesian coordinates? 

message: The article gives a formula, but does not explain how it comes to be in the first place. I have never studied such a formula, and my attempt to obtain it from the formula I did study (how to obtain the area of a regular polygon) gives me a formula that looks completely different. Here's the reasoning I followed:
* We know that the area of any regolar polygon is equal to P*a/2, where P is the perimeter and a is the apothem.
* In the case of a pentagon, P equals to 5*L, where L is the length of a side, so the surface area of a pentagon is 5*L*a/2
* We also know that the dodecahedron has 12 sides, so a first attempt to a surface area formula for the dodecahedron is 12*5*L*a/2 = 6*5*L*a = 30*L*a
* The apothem of the pentagon equals L*tan(54°)/2, so, if we replace this expression to a in the previous formula, we get 30*L*L*tan(54°)/2, which can be simplified to 15*L2*tan(54°).
The formula so obtained does not even resemble the one in the article. So, where does that one come from? Devil Master (talk) 22:36, 23 November 2011 (UTC)
replies: text: I'm guessing the reduction comes from Exact trigonometric constants#36°: pentagon. Tom Ruen (talk) 22:59, 23 November 2011 (UTC)
thread_title: Surface area - how is the formula obtained?

message: The truncated pentagonal trapezohedron is described here under "topologically identical irregular dodecahedra", but is it the case that one such trapezohedron is actually identical to the regular dodecahedron? If there is actually a whole family of these, which are generally irregular, but regular in one special case, I think this could be more clearly explained. Also, it would be nice to have a picture of an example that was more obviously different from the regular dodecahedron. As it is, the two look unhelpfully similar. 86.171.43.159 (talk) 03:29, 30 July 2012 (UTC)
thread_title:  Truncated pentagonal trapezohedron  

message: I believe there is an additional projection of the dodecahedron. The edge view of the dodecahedron would be the view with and edge closest and perpendicular to the viewer. I have drawn this by hand and it seems to be a valid projection. I have based this on the edge projection shown on the icosahedron page. I do not know what constitutes "special" orthogonal projections. So I cannot say whether this projection is valid. I can only say that the resulting image is highly symmetrical and similar to the one seen for the icosahedron. I assume the projection is valid here if it is also valid for the icosahedron. Others will need to verify that the projection is "special" enough and if so, then also, someone will need to create the image to look similar to the existing ones.  Here is a hand drawn image with sample dimension: 
. 
I should mention that the dimensions in the diagram are: 1, Phi/2, Phi^2, cos 18 and cos 54 (degrees). — Preceding unsigned comment added by Peawormsworth (talk • contribs) 08:24, 28 October 2012 (UTC)
replies: text: I added an image . SockPuppetForTomruen (talk) 21:45, 29 October 2012 (UTC)
thread_title: Edge orthogonal projection

message: First, a naive question:  If the resistor network section was rehabilitated, why wasn't it restored?
From Tamfang's entry, above:
"There are a few face-transitive (with congruent but irregular faces) dodecahedrons missing from the list
    The ones missing are the octahedral pentagonal dodecahedron, the tetrahedral pentagonal dodecahedron, and the trapezoidal dodecahedron."
That's tetragonal, not tetrahedral.
   "If you look up "Isohedron" on Mathworld, you can see a rotating models of each of them."
No, to rotate you have download the Mathematica notebook.
    "As a side note, I would love to know if the pyritohedron is the same thing as either the octahedral or tetrahedral pentagonal dodecahedron. —Preceding unsigned comment added by 63.72.235.4 (talk) 15:15, 10 February 2009 (UTC)
thread_title:  Other Dodecahedra 

message: The animation could obviate the adjoining concave pyritohedron image if it did not arbitrarily(?) restrict to convex.  In particular, it could include the interesting equilateral "endododecahedron" case.  Also, the animation would be easier on the eyes and less jerky if driven by a sinusoid rather than a triangle wave.  Both of these improvements are (too rapidly?) illustrated in http://gosper.org/pyritodex.gif .  Sat 26 Oct 2013 21:16:47 PDT63.194.69.46 (talk) 04:31, 27 October 2013 (UTC)
replies: text: I made a simple fix, 1/2 second pause on start and middle frames. If you have rights to the pyritodex.gif image it is nice too. Tom Ruen (talk) 04:43, 27 October 2013 (UTC)

text: On your animation, I admit the sinusoidal(?) motion makes me feel nervous, like an alien is going to jump out and kill me. Also I rather prefer the 8 cubic points to remain fixed, while you rescale it smaller as the dodecahedral tents rise. Tom Ruen (talk) 21:40, 30 October 2013 (UTC)

text: Excellent, looks like it could be scaled larger within the frame (or cropped). I'll have to think more on the great stellated dodecahedron connection - what negative h value is that?!  Tom Ruen (talk) 19:34, 31 October 2013 (UTC)

text: p.s. What would be REALLY cool is if the animation had a secondary image to the side, showing the SHAPE of an individual face show in-plane. ALSO it would be great to see a parallel animation dual pseudoicosahedron animation! Tom Ruen (talk) 22:02, 31 October 2013 (UTC)

text: Looks good, just could better crop excess white space? Tom Ruen (talk) 22:22, 31 October 2013 (UTC)

text: I like it with a fixed orientation as-is. Tom Ruen (talk) 03:13, 1 November 2013 (UTC)

text: The slow rotation is okay with me. And now the cropping is very good. Tom Ruen (talk) 06:31, 1 November 2013 (UTC)
thread_title:  Pyritohedron animation

message: The regular dodecahedron main section was moved to its own article (this was done to the icosahedron a while back as well). Most of these wikilinks here  probably need to be changed:  dodecahedron --> dodecahedron. Tom Ruen (talk) 22:29, 10 June 2015 (UTC)
replies: text: It does seem bizarre to move the only dodecahedron that is called a dodecahedron without qualifier to another article with a qualifier and leave everything else here, that is not called simply dodedecahedron. Tom Ruen (talk) 22:48, 10 June 2015 (UTC)
thread_title:  Regular dodecahedron moved

message: The following Wikimedia Commons file used on this page has been nominated for deletion:
* 
Participate in the deletion discussion at the . —Community Tech bot (talk) 17:53, 18 May 2019 (UTC)
thread_title:  A Commons file used on this page has been nominated for deletion 

message: Text and references copied from Armand Spitz to Dodecahedron.  See former article's history for a list of contributors.  7&6=thirteen (☎) 12:30, 3 May 2020 (UTC)
thread_title: Attribution

message: You have added this table six years ago (diff), but you did not clarify what the ratio is supposed to be. I assumed it is the length of the two edge types, but in that case the 1:1 for the concave version is wrong. So what is it? Greetings, Watchduck (quack) 12:57, 31 October 2020 (UTC)
replies: text: I see. Yes, edge length ratio. Why is it wrong? Those are defined as equilateral solutions. Tom Ruen (talk) 14:59, 31 October 2020 (UTC)
replies: text:   Ah, ok. The problem is, that the image shown does not match the numbers. That would be the equilateral endododecahedron in http://gosper.org/pyromania.gif. Could you upload a version where the height is actually -1/phi? (But please do not overwrite :File:Concave pyritohedral dodecahedron.png.) --Watchduck (quack) 16:36, 31 October 2020 (UTC)
thread_title: Special cases of the pyritohedron