File:Dodecahedron vertices.svg

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English: Coordinates of a regular dodecahedron
Right-handed coordinate system with red, green and blue assigned to the same axes

The orange vertices lie at (±1, ±1, ±1) and form a cube (dotted lines).

The red vertices lie at (±ϕ, ±1/ϕ, 0) and form a rectangle on the xy-plane.
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 red, green and blue coordinate triples are circular permutations of each other.)

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.
Date 20:13, 14 March 2024 (UTC)
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current20:13, 14 March 2024Thumbnail for version as of 20:13, 14 March 2024231 × 236 (15 KB)AquitaneHungerForce (talk | contribs){{Information |Description={{en|Coordinates of a {{w|regular dodecahedron}} thumb|Right-handed coordinate system with red, green and blue assigned to the same axes The orange vertices lie at (±1, ±1, ±1) and form a cube (dotted lines). The red vertices lie at (±''ϕ'', ±{{sfrac|1|''ϕ''}}, 0) and form a rectangle on the ''xy''-plane.<br> The green vertices lie at (0, ±''ϕ'', ±{{sfrac|1|''ϕ''}}) and form a rectangle on the ''yz''-plane.<b...

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