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Co-ordinates of a dodecahedron
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!
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!
Answers
Best Answer
No best answer has yet been selected by badhorsey. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.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.
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.
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.
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.
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