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)
It's been a long time since I saw the episode, but I'm pretty sure that the polyhedra in the Star Trek episode were not dodecahedra but something else, either cuboctahedra or rhombicuboctahedra. -- Matt McIrvin 04:04, 31 July 2005 (UTC)
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)
The dodecahedron is one of the most complex, completely symetrical, geometric three-dimensional figures.
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
Suggest correcting the dihedral angle in the table from arccos(-1/5)
to arccos(-1/sqrt(5))
or equivalent.
cadull
21:16, 10 March 2006 (UTC)
I removed this long unsupported statement under "uses":
I stumbled upon this paper [1], 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)
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)
It's fixed now. Someone was trying to be a little too fancy with templates when they made that frame. As a result, it is very hard to edit. The correct page to edit is Template:Reg_polyhedra_db. -- Fropuff 18:05, 13 November 2006 (UTC)
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)
This following section was removed. I moved it here for reference.
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:
Somebody please verify this, find a citation, and integrate it into the article. Thanks.— Tetracube ( talk) 03:18, 30 March 2009 (UTC)
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) —Preceding unsigned comment added by 80.168.224.185 ( talk)
In the new section "Dimensions" (thanks), the radius of the insphere is given as . It could be put in lower terms as . Any strong preferences either way? — Tamfang ( talk) 17:50, 23 February 2010 (UTC)
Is it really bigger than an icosahedron when made to fit in a sphere? References/Math? Simanos ( talk) 15:32, 1 March 2010 (UTC)
It is Sqrt[1/6 (5+Sqrt[5])] times bigger than an icosahedron:
Volume of Dodecahedron normalized by the volume of the circumscribed sphere is:
Sqrt[5/6 (3+Sqrt[5])]/\[Pi]
Volume of Icosahedron normalized by the volume of the circumscribed sphere is:
Sqrt[1/2 (5+Sqrt[5])]/\[Pi]
Divide them and you get:
Sqrt[1/6 (5+Sqrt[5])]
Roughly:
1.09818547139510923450322671904 — Preceding
unsigned comment added by
84.85.32.196 (
talk)
18:11, 13 May 2012 (UTC)
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)
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)
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)
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:
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)
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)
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)
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)
(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)"
Yes, "octahedral pentagonal dodecahedron" and pyritohedron are both (rather unsuitable) names for that continuum of solids. See http://gosper.org/pyrominia.gif .
Which points out another EQUILATERAL pyritohedron--the endododecahedron (J.H.Conway et al., the Symmetries of Things, p. 328). Briefly, circumscribe the black cubes of an infinite 3D checkerboard with regular dodecahedra. The complement is endododecahedra inscribed in all the white cubes. Endododecahedron deserves mention after the regular dodecahedron section.
And there is yet another equilateral pentagonal dodecahedron! http://gosper.org/pentiprisms.png , third figure, top row. And http://gosper.org/pentatrapezohedra.gif This was discovered a few years ago by a homeschooled boy, Julian Ziegler Hunts, who deems it too trivial to publish.
If we discard something trivial (in retrospect) for being "original research", the article will perpetuate the false impression that there are only two equilateral pentagonal dodecahedra (assuming we cover endododecahedron).
But how do we cover Julian's polyhedron, which lacks even a name? Equilateral overtruncated pentatrapezohedron? Concave pentagonal pentiprism? (Like antiprism, but with pentagons instead of equilateral triangles. The convex ones are truncated trapezohedra.) Could we add an "overtruncated" section to truncated trapezohedron without committing original research?
It's possible that some of this nomenclature is settled in the Conway book, which I have yet to see.
If we can settle the nomenclature and extend truncated trapezohedron, I would propose this cleanup of the Other dodecahedra section:
Topologically distinct dodecahedra include:
...
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
Bill Gosper ( talk) 08:12, 2 November 2013 (UTC)
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 PDT 63.194.69.46 ( talk) 04:31, 27 October 2013 (UTC)
That helps a lot. Yes, I made pyritodex.gif and "advertised" it to the math-fun list. I hereby(?) relinquish all rights to it, but it is below Wikipedia's graphics standards, I think. I can try sprucing it up, if you wish. Bill Gosper ( talk) 21:12, 30 October 2013 (UTC)
Good points. Can we get away with http://gosper.org/pyredohedra.gif, or is explaining how a stellated icosahedron is an extreme pyritohedron too much like original research? Bill Gosper ( talk) 12:53, 31 October 2013 (UTC) Oops, the Great_stellated_dodecahedron article claims this is one. That should be easier to explain. Bill Gosper ( talk) 14:00, 31 October 2013 (UTC)
I'll consider these. Meanwhile, what do you think of http://gosper.org/pyromania.gif ? 71.146.130.17 ( talk) 22:18, 31 October 2013 (UTC)
The only way I can coax that out of Mathematica is to rasterize (= degrade) and then crop: http://gosper.org/pyrominia.gif ListAnimate[
Table[ImageCrop[ Graphics3D[{Red, Polygon[Join[#, -#] &@ Join[#, Map[RotateLeft, #, {2}], Map[RotateRight, #, {2}]] &@{#, {-1, 1, -1}*# & /@ #} &[{{-(1/2) + 2 z^2, -(1/2) + z, 0}, {-(1/2), -(1/2), -(1/2)}, {0, -(1/2) + 2 z^2, -(1/2) + z}, {1/2, -(1/2), -(1/2)}, {1/2 - 2 z^2, -(1/2) + z, 0}}]], Black, T[z]}, PlotRange -> 1, Boxed -> False, ImageSize -> {600, 750}] /. z -> %212 /. T[x_] :> Text[Style[pyritext[x], Large], {1/2, -3/4, -3/4}] /. pyritext[_] -> "", {409, 500}], {t, 1, 17, 1/8}], AnimationRunning -> True, AnimationDirection -> ForwardBackward]
%212 is a computed Piecewise. The centering shouldn't be hard to fix. Maybe the object should rotate slowly while paused?
Regarding your negative h value question, my parameter is "z" and is (quite) positive for the great stellated ...: pyritext[-1/2] = "rhombic
dodecahedron"; pyritext[(1 - Sqrt[5])/4] = "regular dodecahedron"; pyritext[0] = "cubically degenerate pyritohedron"; pyritext[(Sqrt[5] - 1)/4] = "(equilateral) endododecahedron"; pyritext[.501] = "axes-degenerate pyritohedron"; pyritext[(1 + Sqrt[5])/4] = "great stellated dodecahedron"; 71.146.130.17 ( talk) 02:38, 1 November 2013 (UTC)
Oops, I just overwrote http://gosper.org/pyrominia.gif with some movement. The moving text was an accident I kind of like. Are you sure you hate it? Anyway, the zoom solution is ViewAngle. 71.146.130.17 ( talk) 05:45, 1 November 2013 (UTC)
@ Bill Gosper: If you release the rights to http://gosper.org/pyredohedra.gif and http://gosper.org/pyromania.gif, I would like to upload them to Commons. Woud that be okay? 13:17, 31 October 2020 (UTC)
Is it worth spinning the Regular dodecahedron off to its own article, as has now been done for the regular icosahedron? — Cheers, Steelpillow ( Talk) 13:27, 18 September 2014 (UTC)
In the list under Other dodecahedra/Uniform polyhedra one finds:
all with 14 faces. — Preceding unsigned comment added by Episcophagus ( talk • contribs) 10:40, 1 October 2014 (UTC)
You might add to the history section that Plato refers to balls being made of 12 pieces of leather in Phaedo 110B8 — Preceding unsigned comment added by 86.174.106.137 ( talk • contribs)
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 [5] probably need to be changed: [[dodecahedron]] --> [[regular dodecahedron|dodecahedron]]. Tom Ruen ( talk) 22:29, 10 June 2015 (UTC)
The following Wikimedia Commons file used on this page has been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 17:53, 18 May 2019 (UTC)
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)
@ Tomruen: 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)
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)
It's been a long time since I saw the episode, but I'm pretty sure that the polyhedra in the Star Trek episode were not dodecahedra but something else, either cuboctahedra or rhombicuboctahedra. -- Matt McIrvin 04:04, 31 July 2005 (UTC)
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)
The dodecahedron is one of the most complex, completely symetrical, geometric three-dimensional figures.
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
Suggest correcting the dihedral angle in the table from arccos(-1/5)
to arccos(-1/sqrt(5))
or equivalent.
cadull
21:16, 10 March 2006 (UTC)
I removed this long unsupported statement under "uses":
I stumbled upon this paper [1], 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)
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)
It's fixed now. Someone was trying to be a little too fancy with templates when they made that frame. As a result, it is very hard to edit. The correct page to edit is Template:Reg_polyhedra_db. -- Fropuff 18:05, 13 November 2006 (UTC)
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)
This following section was removed. I moved it here for reference.
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:
Somebody please verify this, find a citation, and integrate it into the article. Thanks.— Tetracube ( talk) 03:18, 30 March 2009 (UTC)
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) —Preceding unsigned comment added by 80.168.224.185 ( talk)
In the new section "Dimensions" (thanks), the radius of the insphere is given as . It could be put in lower terms as . Any strong preferences either way? — Tamfang ( talk) 17:50, 23 February 2010 (UTC)
Is it really bigger than an icosahedron when made to fit in a sphere? References/Math? Simanos ( talk) 15:32, 1 March 2010 (UTC)
It is Sqrt[1/6 (5+Sqrt[5])] times bigger than an icosahedron:
Volume of Dodecahedron normalized by the volume of the circumscribed sphere is:
Sqrt[5/6 (3+Sqrt[5])]/\[Pi]
Volume of Icosahedron normalized by the volume of the circumscribed sphere is:
Sqrt[1/2 (5+Sqrt[5])]/\[Pi]
Divide them and you get:
Sqrt[1/6 (5+Sqrt[5])]
Roughly:
1.09818547139510923450322671904 — Preceding
unsigned comment added by
84.85.32.196 (
talk)
18:11, 13 May 2012 (UTC)
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)
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)
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)
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:
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)
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)
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)
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)
(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)"
Yes, "octahedral pentagonal dodecahedron" and pyritohedron are both (rather unsuitable) names for that continuum of solids. See http://gosper.org/pyrominia.gif .
Which points out another EQUILATERAL pyritohedron--the endododecahedron (J.H.Conway et al., the Symmetries of Things, p. 328). Briefly, circumscribe the black cubes of an infinite 3D checkerboard with regular dodecahedra. The complement is endododecahedra inscribed in all the white cubes. Endododecahedron deserves mention after the regular dodecahedron section.
And there is yet another equilateral pentagonal dodecahedron! http://gosper.org/pentiprisms.png , third figure, top row. And http://gosper.org/pentatrapezohedra.gif This was discovered a few years ago by a homeschooled boy, Julian Ziegler Hunts, who deems it too trivial to publish.
If we discard something trivial (in retrospect) for being "original research", the article will perpetuate the false impression that there are only two equilateral pentagonal dodecahedra (assuming we cover endododecahedron).
But how do we cover Julian's polyhedron, which lacks even a name? Equilateral overtruncated pentatrapezohedron? Concave pentagonal pentiprism? (Like antiprism, but with pentagons instead of equilateral triangles. The convex ones are truncated trapezohedra.) Could we add an "overtruncated" section to truncated trapezohedron without committing original research?
It's possible that some of this nomenclature is settled in the Conway book, which I have yet to see.
If we can settle the nomenclature and extend truncated trapezohedron, I would propose this cleanup of the Other dodecahedra section:
Topologically distinct dodecahedra include:
...
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
Bill Gosper ( talk) 08:12, 2 November 2013 (UTC)
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 PDT 63.194.69.46 ( talk) 04:31, 27 October 2013 (UTC)
That helps a lot. Yes, I made pyritodex.gif and "advertised" it to the math-fun list. I hereby(?) relinquish all rights to it, but it is below Wikipedia's graphics standards, I think. I can try sprucing it up, if you wish. Bill Gosper ( talk) 21:12, 30 October 2013 (UTC)
Good points. Can we get away with http://gosper.org/pyredohedra.gif, or is explaining how a stellated icosahedron is an extreme pyritohedron too much like original research? Bill Gosper ( talk) 12:53, 31 October 2013 (UTC) Oops, the Great_stellated_dodecahedron article claims this is one. That should be easier to explain. Bill Gosper ( talk) 14:00, 31 October 2013 (UTC)
I'll consider these. Meanwhile, what do you think of http://gosper.org/pyromania.gif ? 71.146.130.17 ( talk) 22:18, 31 October 2013 (UTC)
The only way I can coax that out of Mathematica is to rasterize (= degrade) and then crop: http://gosper.org/pyrominia.gif ListAnimate[
Table[ImageCrop[ Graphics3D[{Red, Polygon[Join[#, -#] &@ Join[#, Map[RotateLeft, #, {2}], Map[RotateRight, #, {2}]] &@{#, {-1, 1, -1}*# & /@ #} &[{{-(1/2) + 2 z^2, -(1/2) + z, 0}, {-(1/2), -(1/2), -(1/2)}, {0, -(1/2) + 2 z^2, -(1/2) + z}, {1/2, -(1/2), -(1/2)}, {1/2 - 2 z^2, -(1/2) + z, 0}}]], Black, T[z]}, PlotRange -> 1, Boxed -> False, ImageSize -> {600, 750}] /. z -> %212 /. T[x_] :> Text[Style[pyritext[x], Large], {1/2, -3/4, -3/4}] /. pyritext[_] -> "", {409, 500}], {t, 1, 17, 1/8}], AnimationRunning -> True, AnimationDirection -> ForwardBackward]
%212 is a computed Piecewise. The centering shouldn't be hard to fix. Maybe the object should rotate slowly while paused?
Regarding your negative h value question, my parameter is "z" and is (quite) positive for the great stellated ...: pyritext[-1/2] = "rhombic
dodecahedron"; pyritext[(1 - Sqrt[5])/4] = "regular dodecahedron"; pyritext[0] = "cubically degenerate pyritohedron"; pyritext[(Sqrt[5] - 1)/4] = "(equilateral) endododecahedron"; pyritext[.501] = "axes-degenerate pyritohedron"; pyritext[(1 + Sqrt[5])/4] = "great stellated dodecahedron"; 71.146.130.17 ( talk) 02:38, 1 November 2013 (UTC)
Oops, I just overwrote http://gosper.org/pyrominia.gif with some movement. The moving text was an accident I kind of like. Are you sure you hate it? Anyway, the zoom solution is ViewAngle. 71.146.130.17 ( talk) 05:45, 1 November 2013 (UTC)
@ Bill Gosper: If you release the rights to http://gosper.org/pyredohedra.gif and http://gosper.org/pyromania.gif, I would like to upload them to Commons. Woud that be okay? 13:17, 31 October 2020 (UTC)
Is it worth spinning the Regular dodecahedron off to its own article, as has now been done for the regular icosahedron? — Cheers, Steelpillow ( Talk) 13:27, 18 September 2014 (UTC)
In the list under Other dodecahedra/Uniform polyhedra one finds:
all with 14 faces. — Preceding unsigned comment added by Episcophagus ( talk • contribs) 10:40, 1 October 2014 (UTC)
You might add to the history section that Plato refers to balls being made of 12 pieces of leather in Phaedo 110B8 — Preceding unsigned comment added by 86.174.106.137 ( talk • contribs)
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 [5] probably need to be changed: [[dodecahedron]] --> [[regular dodecahedron|dodecahedron]]. Tom Ruen ( talk) 22:29, 10 June 2015 (UTC)
The following Wikimedia Commons file used on this page has been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 17:53, 18 May 2019 (UTC)
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)
@ Tomruen: 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)