The great rhombicosidodecahedron is the 62-faced Archimedean solid with faces . It is also known as the rhombitruncated
icosidodecahedron, and is sometimes improperly called the truncated icosidodecahedron
(Ball and Coxeter 1987, p. 143; Maeder 1997; Conway et al. 1999), a name
which is inappropriate since truncation would yield
rectangular instead of square.
It is illustrated above together with a wireframe version and a net
that can be used for its construction.
It is also the uniform polyhedron with Maeder index 28 (Maeder 1997), Wenninger index 16 (Wenninger 1989), Coxeter index 31 (Coxeter
et al. 1954), and Har'El index 33 (Har'El 1993). It has Schläfli
symbol t and Wythoff symbol .
Some symmetric projections of the great rhombicosidodecahedron are illustrated above.
The great rhombicosidodecahedron constructed by E. K. Herrstrom in origami is illustrated above (Kasahara and Takahama 1987, pp. 46-49). This construction
uses 900 sonobè units, each made from a single sheet of origami paper.
Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987.Conway,
J. H.; Radin, C.; and Sadun, L. "On Angles Whose Squared Trigonometric
Functions Are Rational." Discr. Computat. Geom.22, 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. "Great Rhombicosidodecahedron or
Truncated Icosidodecahedron. ." §3.7.12 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 112-113, 1989.Geometry
Technologies. "Rhombitruncated Icosidodecahedron." http://www.scienceu.com/geometry/facts/solids/rh_tr_icosidodeca.html.Har'El,
Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata47,
57-110, 1993.Kasahara, K. and Takahama, T. Origami
for the Connoisseur. Tokyo: Japan Publications, 1987.Kasahara,
K. "The Final Semiregular Polyhedron." Origami
Omnibus: Paper-Folding for Everyone. Tokyo: Japan Publications, p. 229,
1988.Maeder, R. E. "28: Truncated Icosidodecahedron."
1997. https://www.mathconsult.ch/static/unipoly/28.html.Wenninger,
M. J. "The Rhombitruncated Icosidodecahedron." Model 16 in Polyhedron
Models. Cambridge, England: Cambridge University Press, p. 30, 1989.