Editing Icosidodecahedron (section)

== Construction ==
One way to construct the icosidodecahedron is to start with two [[pentagonal rotunda]] by attaching them to their bases. These rotundas cover their decagonal base so that the resulting polyhedron has 32 faces, 30 vertices, and 60 edges. This construction is similar to one of the [[Johnson solids]], the [[pentagonal orthobirotunda]]. The difference is that the icosidodecahedron is constructed by twisting its rotundas by 36°, a process known as [[gyration]], resulting in the pentagonal face connecting to the triangular one. The icosidodecahedron has an alternative name, ''pentagonal gyrobirotunda''.{{r|berman|os}}
{{multiple image
 | image1 = Icosidodecahedron.png
 | image2 = Dissected icosidodecahedron.png
 | image3 = Pentagonal orthobirotunda solid.png
 | footer = The difference between icosidodecahedron and pentagonal orthobirotunda, and its dissection.
 | align = center
 | total_width = 400
}}

There is another way to construct it, and that is [[Rectification (geometry)|rectification]] of an [[Icosahedron]] or a [[Dodecahedron]].

Convenient [[Cartesian coordinates]] for the vertices of an icosidodecahedron with unit edges are given by the [[even permutation]]s of:
<math display="block"> (\pm 1, 0, 0), \qquad \tfrac{1}{2}\left(\pm \varphi, \pm \tfrac{1}{\varphi}, \pm 1 \right), </math>
where <math> \varphi </math> denotes the [[golden ratio]].{{r|dm}}