Talk:Regular dodecahedron

Wording of surface area and volume calculations
The wording currently reads: "Additionally, the surface area and volume of a regular dodecahedron are related to the golden ratio. A dodecahedron with an edge length of one unit has the properties:". I believe "A dodecahedron" should be changed to "A regular dodecahedron" because the formulas quoted there do not apply to generic dodecahedrons. Those formulas are


 * $${\displaystyle A = \frac{15\varphi}{\sqrt{3-\varphi}}}$$
 * $${\displaystyle V = \frac{5\varphi^3}{6-2\varphi}}$$

Someone can create a regular dodecahedron with the coordinates in Dodecahedron by setting h = $−1 + \sqrt{5}⁄2$, the reciprocal of the golden ratio. The formulas above only work for this special value and hence I propose the wording change I just mentioned.

--Zenulabidin2k (talk) 20:26, 21 May 2020 (UTC)

Facet defining equations of regular dodecahedron
If the facet defining equations should describe a dodecahedron with cartesian coordinates given in the paragraph before, I suppose they do not have the right scale! It can be easily checked that the distance of two parallel planes described by these equations is $$ 2r_i=\frac{2}{ \sqrt{\phi^4+\phi^2}} =\frac{2}{\phi^2 \sqrt{3-\phi}}$$ and the edge length $$ a =\frac{2}{\phi^4}$$. However faces of a dodecahedron with edge length $$ a =\frac{2}{\phi}$$ are obviously defined by the following equations


 * ϕx ± y = ±ϕ2
 * ϕy ± z = ±ϕ2
 * ϕz ± x = ±ϕ2

or with arbitrary edge length $$ a $$
 * ϕx ± y = ±aϕ3/2
 * ϕy ± z = ±aϕ3/2
 * ϕz ± x = ±aϕ3/2

— Preceding unsigned comment added by StefanDoc (talk • contribs) 13:33, 11 July 2016 (UTC)


 * It looks like the section was added by one anonymous editor diff October 16, 2015, and changed by another diff November 11, 2015, with no references. Tom Ruen (talk) 14:06, 11 July 2016 (UTC)

Failed to parse MathML
Under the Surface area and volume heading, the equation A = is getting a Failed to parse. I'm on a Mac with latest Safari & Firefox.

Surface area and volume[edit] The surface area A and the volume V of a regular dodecahedron of edge length a are:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle A =

It does not seem to happen on the previous version, or on my iPhone. Also, if I edit the page and push Preview, it does not display?? Will check from Windows.

Bodysurfinyon (talk) 04:00, 16 July 2018 (UTC)

Vertex definition = ?
I am referring to this

(±1, ±1, ±1)    (0, ±ϕ, ±1/ϕ) (±1/ϕ, 0, ±ϕ) (±ϕ, ±1/ϕ, 0) I can't understand it. A dodecahedron is composed of twelve regular pentagonal faces.

How can 4 points define a pentagonal face???

Thanks!

I appreciate it. — Preceding unsigned comment added by Chrisir (talk • contribs) 21:11, 12 January 2019 (UTC)

I used the other explanation now : Vertex coordinates: The orange vertices lie at (±1, ±1, ±1) and form a cube (dotted lines). The green vertices lie at (0, ±ϕ, ±1/ϕ) and form a rectangle on the yz-plane. The blue vertices lie at (±1/ϕ, 0, ±ϕ) and form a rectangle on the xz-plane. The pink vertices lie at (±ϕ, ±1/ϕ, 0) and form a rectangle on the xy-plane. The distance between adjacent vertices is 2/ϕ, and the distance from the origin to any vertex is √3. ϕ = (1 + √5)/2 is the golden ratio. — Preceding unsigned comment added by Chrisir (talk • contribs) 13:37, 13 January 2019 (UTC)

I found this


 * Pentagon #1 : [ -0.618034, 0.0, 1.618034 ][ 0.618034, 0.0, 1.618034 ][ 1.0, 1.0, 1.0 ][ 0.0, 1.618034, 0.618034 ][ -1.0, 1.0, 1.0 ]
 * Pentagon #2 : [ 0.618034, 0.0, 1.618034 ][ 1.0, 1.0, 1.0 ][ 1.618034, 0.618034, 0.0 ][ 1.618034, -0.618034, 0.0 ][ 1.0, -1.0, 1.0 ]
 * Pentagon #3 : [ 1.0, 1.0, 1.0 ][ 0.0, 1.618034, 0.618034 ][ 0.0, 1.618034, -0.618034 ][ 1.0, 1.0, -1.0 ][ 1.618034, 0.618034, 0.0 ]
 * Pentagon #4 : [ -1.0, 1.0, 1.0 ][ -1.618034, 0.618034, 0.0 ][ -1.0, 1.0, -1.0 ][ 0.0, 1.618034, -0.618034 ][ 0.0, 1.618034, 0.618034 ]
 * Pentagon #5 : [ 0.0, 1.618034, -0.618034 ][ -1.0, 1.0, -1.0 ][ -0.618034, 0.0, -1.618034 ][ 0.618034, 0.0, -1.618034 ][ 1.0, 1.0, -1.0 ]
 * Pentagon #6 : [ 1.618034, 0.618034, 0.0 ][ 1.0, 1.0, -1.0 ][ 0.618034, 0.0, -1.618034 ][ 1.0, -1.0, -1.0 ][ 1.618034, -0.618034, 0.0 ]
 * Pentagon #7 : [ -1.618034, -0.618034, 0.0 ][ -1.618034, 0.618034, 0.0 ][ -1.0, 1.0, -1.0 ][ -0.618034, 0.0, -1.618034 ][ -1.0, -1.0, -1.0 ]
 * Pentagon #8 : [ -0.618034, 0.0, 1.618034 ][ -1.0, 1.0, 1.0 ][ -1.618034, 0.618034, 0.0 ][ -1.618034, -0.618034, 0.0 ][ -1.0, -1.0, 1.0 ]
 * Pentagon #9 : [ -1.0, -1.0, -1.0 ][ -0.618034, 0.0, -1.618034 ][ 0.618034, 0.0, -1.618034 ][ 1.0, -1.0, -1.0 ][ 0.0, -1.618034, -0.618034 ]
 * Pentagon #10 : [ -1.0, -1.0, 1.0 ][ -1.618034, -0.618034, 0.0 ][ -1.0, -1.0, -1.0 ][ 0.0, -1.618034, -0.618034 ][ 0.0, -1.618034, 0.618034 ]
 * Pentagon #11 : [ 1.0, -1.0, 1.0 ][ 0.0, -1.618034, 0.618034 ][ 0.0, -1.618034, -0.618034 ][ 1.0, -1.0, -1.0 ][ 1.618034, -0.618034, 0.0 ]
 * Pentagon #12 : [ 0.618034, 0.0, 1.618034 ][ -0.618034, 0.0, 1.618034 ][ -1.0, -1.0, 1.0 ][ 0.0, -1.618034, 0.618034 ][ 1.0, -1.0, 1.0 ]
 * — Preceding unsigned comment added by Chrisir (talk • contribs) 13:40, 13 January 2019 (UTC)