Talk:Dodecahedron

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By far the worst of the solids. Who the hell thought up this lame excuse for a polyhedron?

Despite years of oppression at the hands of fringe Alaskan separatist groups, the dodecahedron has played an integral roll (ha!) in calculating the damage caused by common Wizard spells such as Arcane Frost (4d12), Charming Immolation (6d12), and Power Word Kill Alaskan (60d12).

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)

There are some pictures here; it's a cuboctahedron. Should probably delete the trivia item. --Matt McIrvin 04:11, 31 July 2005 (UTC)

Contents

[edit] Dodecahedron Canonical coordinates

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 20 vertices are hidden in the sign permutations. (±?,?,?) has two values. (±?,±?,?) has 4 (2x2) value permutations and (±?,±?,±?) has 8 (2x2x2) permutations. So the above paragraph lists 4+4+4+8=20 vertices. Tom Ruen 23:55, 8 December 2005 (UTC)

The dodecahedron is one of the most complex, completely symetrical, geometric three-dimensional figures.

[edit] New stat table

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)

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)


[edit] Electrical resistance

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 [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)

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)

[edit] Dihedral angle in the frame

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 π − 2ψ where ψ is defined by:
cos(ψ) = csc(π / 5)cos(π / 3) = cos(π / 3) / sin(π / 5)
(This is from Coxeter's Regular Polytopes.)—Tetracube 17:54, 13 November 2006 (UTC)

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)


[edit] Uses Vs Trivia

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)