Starting with

End up with

Pentagon

Pentagonal Cupola

Decagon

Pentagonal Cupola

Octagon

Square Cupola

Cube

Square Cupola

Cube

Square Orthobicupola

Square Cupola

Small Rhombicuboctahedron

Three Regular Tetrahedra

Triangular Cupola

Tetrahedron

Triangular Cupola

Tetrahedron

Cuboctahedron

Three Hexagons

Cuboctahedron

Six Tetrahedra

Truncated Tetrahedron

Hexagon

Truncated Octahedron

Five Octahedra

Icosidodecahedron

Dodecahedron

Truncated Icosidodecahedron

Dodecahedron

Rhombic Dodecahedron

Dodecahedron

Rhombic Icosahedron

Dodecahedron

Rhombic Triacontahedron

Pentagonal Cupola

Small Rhombicosidodecahedron

Five Decagons

Icosidodecahedron

Dodecahedron

Pantakis Dodecahedron

Dodecahedron

Intersection of Five Octahedra

Octagon

Deltoidal Icositetrahedron

XYZ-Box

Deltoidal Icositetrahedron

Small Rhombicuboctahedron

Great Rhombicuboctahedron