For sake of completeness I list all "uniform polyhedra", which include the platonic and archimedean solids but additionally cover als the concave (non-convex) polyhedra which aren't suitable for habitat development.
Tetrahedron
Truncated Tetrahedron
Octahemioctahedron
Tetrahemihexahedron
Octahedron
Cube
Cuboctahedron
Truncated Octahedron
Truncated Cube
Rhombicuboctahedron
Truncated Cuboctahedron
Snub Cube
Small Cubicuboctahedron
Great Cubicuboctahedron
Cubohemioctahedron
Cubitruncated Cuboctahedron
Great Rhombicuboctahedron
Small Rhombihexahedron
Stellated Truncated Hexahedron
Great Truncated Cuboctahedron
Great Truncated Cuboctahedron
Icosahedron
Dodecahedron
Icosidodecahedron
Truncated Icosahedron
Truncated Dodecahedron
Rhombicosidodecahedron
Truncated Icosidodecahedron
Snub Dodecahedron
Small Ditrigonal Icosidodecahedron
Small Icosicosidodecahedron
Small Snub Icosicosidodecahedron
Small dodecicosidodecahedron
Small Stellated Dodecahedron
Great Dodecahedron
Dodecadodecahedron
Truncated Great Dodecahedron
Rhombidodecadodecahedron
Small Rhombidodecahedron
Snub Dodecadodecahedron
Ditrigonal Dodecadodecahedron
Great Ditrigonal Dodecicosidodecahedron
Small Ditrigonal Dodecicosidodecahedron
Icosidodecadodecahedron
Icositruncated Dodecadodecahedron
Snub Icosidodecadodecahedron
Great Ditrigonal Icosidodecahedron
Great Icosicosidodecahedron
Small Icosihemidodecahedron
Small Dodecicosahedron
Small Dodecahemidodecahedron
Great Stellated Dodecahedron
Great Icosahedron
Great Icosidodecahedron
Great Truncated Icosahedron
Rhombicosahedron
Great Snub Icosidodecahedron
Small Stellated Truncated Dodecahedron
Truncated Dodecadodecahedron
Inverted Snub Dodecadodecahedron
Great Dodecicosidodecahedron
Small Dodecahemicosahedron
Great Dodecicosahedron
Great Snub Dodecicosidodecahedron
Great Dodecahemicosahedron
Great Stellated Truncated Dodecahedron
Great Rhombicosidodecahedron
Great Truncated Icosidodecahedron
Great Inverted Snub Icosidodecahedron
Great Dodecahemidodecahedron
Great Icosihemidodecahedron
Small Retrosnub Icosicosidodecahedron
Great Rhombidodecahedron
Great Retrosnub Icosidodecahedron
Great Dirhombicosidodecahedron
Pentagonal Prism
Pentagonal Antiprism
Pentagrammic Prism
Pentagrammic Antiprism
Pentagrammic Crossed Antiprism