Starting with
End up with
Pentagon
Pentagonal Cupola
Decagon
Octagon
Square Cupola
Cube
Square Orthobicupola
Small Rhombicuboctahedron
Three Regular Tetrahedra
Triangular Cupola
Tetrahedron
Cuboctahedron
Three Hexagons
Six Tetrahedra
Truncated Tetrahedron
Hexagon
Truncated Octahedron
Five Octahedra
Icosidodecahedron
Dodecahedron
Truncated Icosidodecahedron
Rhombic Dodecahedron
Rhombic Icosahedron
Rhombic Triacontahedron
Small Rhombicosidodecahedron
Five Decagons
Pantakis Dodecahedron
Intersection of Five Octahedra
Deltoidal Icositetrahedron
XYZ-Box
Great Rhombicuboctahedron