The image of 
in the special orthogonal group 
, where 
is the icosahedral group.
Bipolyhedral Group
See also
Icosahedral Group, Special Orthogonal GroupExplore with Wolfram|Alpha
References
Endraß, S. "The Sarti Surface." http://enriques.mathematik.uni-mainz.de/docs/Esarti.shtml.Referenced on Wolfram|Alpha
Bipolyhedral GroupCite this as:
Weisstein, Eric W. "Bipolyhedral Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BipolyhedralGroup.html