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