The truncated dodecahedral graph is the cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated dodecahedron.
It is implemented in the Wolfram Language as GraphData["TruncatedDodecahedralGraph"].
It has LCF notation [30, , 2, 21,
, 2, 12,
, 2,
,
, 2,
,
, 2, 30,
, 2,
,
, 2, 21,
, 2,
,
, 2, 12,
,
.