The rhombicosahedron is the uniform polyhedron with Maeder index 56 (Maeder 1997), Wenninger index 96 (Wenninger 1989), Coxeter
index 72 (Coxeter et al. 1954), and Har'El index 61 (Har'El 1993). It has
Wythoff symbol and its faces are .
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.Har'El, Z. "Uniform
Solution for Uniform Polyhedra." Geometriae Dedicata47, 57-110,
1993.Maeder, R. E. "56: Rhombicosahedron." 1997. https://www.mathconsult.ch/static/unipoly/56.html.Wenninger,
M. J. "Rhombicosahedron." Model 96 in Polyhedron
Models. Cambridge, England: Cambridge University Press, pp. 149-150,
1971.
and its faces are 
.
"Coxeter", 72
], UniformPolyhedron[
"Kaleido", 61
], UniformPolyhedron[
"Uniform", 56
], or UniformPolyhedron[
"Wenninger", 96
]. It is also implemented in the Wolfram
Language as PolyhedronData["Rhombicosahedron"].
