The truncated dodecahedron is the 32-faced Archimedean solid with faces . It is also uniform
polyhedron with Maeder index 26 (Maeder 1997), Wenninger index 10 (Wenninger
1989), Coxeter index 29 (Coxeter et al. 1954), and Har'El index 31 (Har'El
1993). It has Schläfli symbol t and Wythoff symbol . It is illustrated above together
with a wireframe version and a net that can be used for its
construction.

Some symmetric projections of the truncated dodecahedron are illustrated above.

To construct the truncated dodecahedron by truncation, note that we want the inradius of the truncated pentagon to correspond with that of
the original pentagon, , of unit side length . This means that the side lengths of the decagonal faces in the truncated dodecahedron
satisfy

(1)

giving

(2)

The length of the corner which is chopped off is therefore given by

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321-332, 1999.Coxeter, H. S. M.; Longuet-Higgins, M. S.;
and Miller, J. C. P. "Uniform Polyhedra." Phil. Trans. Roy.
Soc. London Ser. A246, 401-450, 1954.Cundy, H. and Rollett,
A. "Truncated Dodecahedron. ." §3.7.9 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 109, 1989.Geometry
Technologies. "Truncated Dodecahedron." http://www.scienceu.com/geometry/facts/solids/tr_dodeca.html.Har'El,
Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata47,
57-110, 1993.Kasahara, K. "The Final Semiregular Polyhedron."
Origami
Omnibus: Paper-Folding for Everyone. Tokyo: Japan Publications, p. 229,
1988.Maeder, R. E. "26: Truncated Dodecahedron." 1997.
https://www.mathconsult.ch/static/unipoly/26.html.Wenninger,
M. J. "The Truncated Dodecahedron." Model 10 in Polyhedron
Models. Cambridge, England: Cambridge University Press, p. 24, 1989.