Void Truncated Icosidodecahedron
 
Void Truncated Icosidodecahedron is a 62 axis twisty puzzle technically shaped in truncated icosidodecahedron (links to wikipedia) then hollowed out using void mechanism. It contains 12 decagonal faces, 20 hexagonal faces and 30 quadrilateral  faces which turns 72*n, 120*n, 180*n degrees respectively.

This puzzle is functionally equivalent to a vertex and edge and face turning dodecahedron (VEFTD) which has never been in existence even in 3D printed version.

Happy cubing !