Talk:Regular dodecahedron

Wording of surface area and volume calculations

Further information: Regular_dodecahedron § Surface_area_and_volume

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#Cartesian_coordinates by setting h = ⁠−1 + √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

Further information: Regular_dodecahedron § Cartesian_coordinates

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)