Editing Dodecahedron (section)

====Cartesian coordinates====
The eight vertices of a cube have the coordinates (±1, ±1, ±1).

The coordinates of the 12 additional vertices are
<big>(</big>0, ±(1 + ''h''), ±(1 − ''h''<sup>2</sup>)<big>)</big>, 
<big>(</big>±(1 + ''h''), ±(1 − ''h''<sup>2</sup>), 0<big>)</big> and
<big>(</big>±(1 − ''h''<sup>2</sup>), 0, ±(1 + ''h'')<big>)</big>.

''h'' is the height of the [[wedge (geometry)|wedge]]<nowiki>-shaped</nowiki> "roof" above the faces of that cube with edge length 2.

An important case is ''h'' = {{sfrac|1|2}} (a quarter of the cube edge length) for perfect natural pyrite (also the pyritohedron in the [[Weaire–Phelan structure]]).

Another one is ''h'' = {{sfrac|1|[[Golden ratio|φ]]}} = 0.618... for the [[regular dodecahedron]]. See section ''[[#Geometric freedom|Geometric freedom]]'' for other cases.

Two pyritohedra with swapped nonzero coordinates are in dual positions to each other like the dodecahedra in the [[compound of two dodecahedra]].

{|
|
{{multiple image |align=left |total_width=440
| image1 = Polyhedron pyritohedron from yellow max.png
| image2 = Polyhedron pyritohedron from red max.png
| image3 = Polyhedron pyritohedron from blue max.png
| footer = Orthographic projections of the pyritohedron with ''h'' = 1/2
}}
|
{{multiple image |align=left |total_width=278
| image1 = Polyhedron pyritohedron max.png
| image2 = Polyhedron 12 pyritohedral max.png
| footer = Heights 1/2 and 1/[[Golden Ratio|''φ'']]
}}
|
|}

{| class="wikitable collapsible collapsed" style="text-align: center;"
!colspan="2"| Animations
|- style="background-color: white;"
|style="width: 350px;"| [[File:Endo-dodecahedron honeycomb.gif|200px]]
|style="width: 350px;"| [[File:Pyritohedron animation.gif|200px]]
|-
| [[Honeycomb (geometry)|Honeycomb]] of alternating convex and concave pyritohedra with heights between ±{{sfrac|1|[[Golden ratio|φ]]}}
| Heights between 0 (cube)<br>and 1 (rhombic dodecahedron)
|}