Editing Truncated dodecahedron (section)

== Properties ==
The surface area <math> A </math> and the volume <math> V </math> of a truncated dodecahedron of edge length <math> a </math> are:{{r|berman}}
<math display="block"> \begin{align}
A &= 5 \left(\sqrt{3}+6\sqrt{5+2\sqrt{5}}\right) a^2 &&\approx 100.991a^2 \\
V &= \frac{5}{12} \left(99+47\sqrt{5}\right) a^3 &&\approx 85.040a^3
\end{align}</math>

The dihedral angle of a truncated dodecahedron between two regular dodecahedral faces is 116.57°, and that between triangle-to-dodecahedron is 142.62°.{{r|johnson}}

[[File:Truncated dodecahedron.stl|thumb|3D model of a truncated dodecahedron]]
The truncated dodecahedron is an [[Archimedean solid]], meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex.<ref name=diudea/> It has the same symmetry as the regular icosahedron, the [[icosahedral symmetry]].<ref name=kk/> The polygonal faces that meet for every vertex are one equilateral triangle and two regular decagon, and the [[vertex figure]] of a truncated dodecahedron is <math> 3 \cdot 10^2 </math>. The dual of a truncated dodecahedron is [[triakis icosahedron]], a [[Catalan solid]],{{r|williams}} which shares the same symmetry as the truncated dodecahedron.{{r|holden}}

The truncated dodecahedron is non-[[Chirality (mathematics)|chiral]], meaning it is congruent to its mirror image.{{r|kk}}