The snub dodecadodecahedron, not to be confused with the Archimdeansnub dodecahedron, is the uniform
polyhedron is the uniform polyhedron with
Maeder index 40 (Maeder 1997), Wenninger index 111 (Wenninger 1989), Coxeter index
49 (Coxeter et al. 1954), and Har'El index 45 (Har'El 1993). It has Wythoff
symbol.
Its faces are .
Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, p. 139, 1987.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. "Snub Dodecahedron. ." §3.7.13 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 114-115, 1989.Har'El,
Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata47,
57-110, 1993.Maeder, R. E. "40: Snub Dodecadodecahedron."
1997. https://www.mathconsult.ch/static/unipoly/40.html.Wenninger,
M. J. "Snub Dodecadodecahedron." Model 111 in Polyhedron
Models. Cambridge, England: Cambridge University Press, pp. 174-176,
1971.
.
Its faces are 
.
"Coxeter",
49
],
UniformPolyhedron[
"Kaleido",
45
],
UniformPolyhedron[
"Uniform",
40
],
or UniformPolyhedron[
"Wenninger",
111
].
It is also implemented in the Wolfram
Language as PolyhedronData["SnubDodecadodecahedron"].
." §3.7.13 in