Solids with full icosahedral symmetry

Platonic solids - regular polyhedra (all faces of the same type) {5,3}{3,5}

Archimedean solids - polyhedra with more than one polygon face type. 3.10.104.6.105.6.63.4.5.43.5.3.5

Catalan solids - duals of the Archimedean solids. V3.10.10V4.6.10V5.6.6V3.4.5.4V3.5.3.5

Platonic solids NamePictureFacesEdgesVerticesEdges per faceFaces meetingat each vertexdodecahedron (Animation)12302053icosahedron (Animation)20301235

Achiral Archimedean solids Name pictureFaces Edges Vertices Vertex configuration icosidodecahedron(quasi-regular: vertex- and edge-uniform) (Video) 32 20 triangles12 pentagons 60 30 3,5,3,5 truncated dodecahedron (Video) 3220 triangles12 decagons 90 60 3,10,10 truncated icosahedronor commonly football (soccer ball) (Video) 32 12 pentagons20 hexagons 90 60 5,6,6 rhombicosidodecahedronor small rhombicosidodecahedron (Video) 62 20 triangles30 squares12 pentagons 120 60 3,4,5,4 truncated icosidodecahedronor great rhombicosidodecahedron (Video) 6230 squares20 hexagons12 decagons 180 120 4,6,10

Achiral Catalan solids NamepictureDual Archimedean solidFacesEdgesVerticesFace Polygonrhombic triacontahedron(quasi-regular dual: face- and edge-uniform)(Video)icosidodecahedron306032rhombustriakis icosahedron(Video)truncated dodecahedron609032isosceles trianglepentakis dodecahedron(Video)truncated icosahedron609032isosceles triangledeltoidal hexecontahedron(Video)rhombicosidodecahedron6012062kitedisdyakis triacontahedronor hexakis icosahedron(Video)truncated icosidodecahedron12018062scalene triangle

Kepler-Poinsot solids

Achiral nonconvex uniform polyhedra

Chiral Archimedean and Catalan solids

Archimedean solids: Name pictureFaces Edges Vertices Vertex configuration snub dodecahedronor snub icosidodecahedron (2 chiral forms) (Video)(Video) 92 80 triangles12 pentagons 150 60 3,3,3,3,5

Catalan solids: NamepictureDual Archimedean solidFacesEdgesVerticesFace Polygonpentagonal hexecontahedron(Video)(Video)snub dodecahedron605092irregular pentagon

Chiral nonconvex uniform polyhedra

Construction

Construction instructions for the following solids are available: Platonic solids, Archimedean solids, Achiral Catalan solids, Kepler–Poinsot solids, Achiral nonconvex uniform polyhedra, Chiral Archimedean and Catalan solids: Snub dodecahedron and Pentagonal hexecontahedron, and Chiral nonconvex uniform polyhedra.

See also The Fifty Nine Icosahedra

Citations

Works cited