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
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Truncated Tetrahedron
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Octahemioctahedron
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Tetrahemihexahedron
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Octahedron
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Cube
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Cuboctahedron
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Truncated Octahedron
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Truncated Cube
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Rhombicuboctahedron
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Truncated Cuboctahedron
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Snub Cube
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Small Cubicuboctahedron
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Great Cubicuboctahedron
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Cubohemioctahedron
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Cubitruncated Cuboctahedron
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Great Rhombicuboctahedron
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Small Rhombihexahedron
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Stellated Truncated Hexahedron
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Great Truncated Cuboctahedron
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Great Truncated Cuboctahedron
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Icosahedron
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Dodecahedron
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Icosidodecahedron
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Truncated Icosahedron
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Truncated Dodecahedron
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Rhombicosidodecahedron
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Truncated Icosidodecahedron
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Snub Dodecahedron
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Small Ditrigonal Icosidodecahedron
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Small Icosicosidodecahedron
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Small Snub Icosicosidodecahedron
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Small dodecicosidodecahedron
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Small Stellated Dodecahedron
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Great Dodecahedron
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Dodecadodecahedron
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Truncated Great Dodecahedron
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Rhombidodecadodecahedron
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Small Rhombidodecahedron
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Snub Dodecadodecahedron
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Ditrigonal Dodecadodecahedron
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Great Ditrigonal Dodecicosidodecahedron
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Small Ditrigonal Dodecicosidodecahedron
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Icosidodecadodecahedron
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Icositruncated Dodecadodecahedron
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Snub Icosidodecadodecahedron
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Great Ditrigonal Icosidodecahedron
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Great Icosicosidodecahedron
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Small Icosihemidodecahedron
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Small Dodecicosahedron
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Small Dodecahemidodecahedron
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Great Stellated Dodecahedron
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Great Icosahedron
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Great Icosidodecahedron
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Great Truncated Icosahedron
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Rhombicosahedron
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Great Snub Icosidodecahedron
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Small Stellated Truncated Dodecahedron
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Truncated Dodecadodecahedron
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Inverted Snub Dodecadodecahedron
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Great Dodecicosidodecahedron
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Small Dodecahemicosahedron
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Great Dodecicosahedron
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Great Snub Dodecicosidodecahedron
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Great Dodecahemicosahedron
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Great Stellated Truncated Dodecahedron
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Great Rhombicosidodecahedron
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Great Truncated Icosidodecahedron
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Great Inverted Snub Icosidodecahedron
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Great Dodecahemidodecahedron
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Great Icosihemidodecahedron
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Small Retrosnub Icosicosidodecahedron
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Great Rhombidodecahedron
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Great Retrosnub Icosidodecahedron
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Great Dirhombicosidodecahedron
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Pentagonal Prism
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Pentagonal Antiprism
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Pentagrammic Prism
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Pentagrammic Antiprism
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Pentagrammic Crossed Antiprism
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