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,
,
.