Wiktionary
great icosihemidodecahedron
n. a polyhedron having 26 faces, 30 vertices, 60 edges, 6 self intersected faces and 6 nonconvex faces
Wikipedia
Great icosihemidodecahedron
In geometry, the great icosihemidodecahedron is a nonconvex uniform polyhedron, indexed as U. Its vertex figure is a crossed quadrilateral.
It is a hemipolyhedron with 6 decagrammic faces passing through the model center.