Co-ordinates of a dodecahedron

[badhorsey]

Hi,

I'm trying to plot a dodecahedron on an ancient 3D program (VU-3D on the ZX Spectrum, in fact).

What I need is a set of co-ordinates for the vertices, either absolute or relative... it doesn't matter which way up it is!

Thanks!

[HowardKennitby]

Is this any good?

http://en.wikipedia.org/wiki/Dodecahedron

[badhorsey]

Thanks, but I know what a dodecahedron is - I just need the co-ordinates of the corners to plot one in three-space.

For example, if I were plotting a 4 x 4 x 4 cube, it would be the following:

0, 0, 0
0, 4, 0
0, 4, 4
0, 0, 4
4, 0, 0
4, 4, 0
4, 4, 4
4, 0, 4

- So I'm looking for the same co-ordinate set for an example dodecahedron.

Size / scale / inversion doesn't matter, I can transpose these.

[vascop]

Hi badhorsey
This link DOES give you the coordinates. There are 20 points in all. Scroll down and you will see them.
The first set of numbers in brackets has 8 combinations, the other three have 4 combinations each giving the total of 8+(3 x 4)=20

[vascop]

Here is an extract from the link given by Howard:

The following Cartesian coordinates define the vertices of a dodecahedron centered at the origin:[1]
(±1, ±1, ±1) [8 combinations]
(0, ±1/φ, ±φ) [4 combinations]
(±1/φ, ±φ, 0) [4 combinations]
(±φ, 0, ±1/φ) [4 combinations]

where φ = (1 + √5) / 2 is the golden ratio (also written τ) ≈ 1.618. The edge length is 2 / φ = √5 – 1. The containing sphere has a radius of √3.

The comments in square brackets are mine.

[badhorsey]

Hi, thanks for that - I saw all of that - but I don't have the mathematical skills to understand it!

[vascop]

OK, here goes:
(1,1,1)
(1,1,-1)
(1,-1,1)
(1,-1,-1)
(-1,1,1)
(-1,1,-1)
(-1,-1,1)
(-1,-1,-1)
(0,0.856,1.168)
(0,0.856,-1.168)
(0,-0.856,1.168)
(0,-0.856,-1.168)
(0.856,1.168,0)
(0.856,-1.168,0)
(-0.856,1.168,0)
(-0.856,-1.168,0)
(0.856,0,1.168)
(0.856,0,-1.168)
(-0.856,0,1.168)
(-0.856,0,-1.168)

[badhorsey]

Thank you!