Uniform polyhedra

geometric shape, a polyhedron with an n-sided polygonal base

thumb|Octagonal antiprism In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .

Archimedean solid

Archimedean solid

The rhombicuboctahedron or small rhombicuboctahedron is a polyhedron with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by Johannes Kepler in his 1618 Harmonices Mundi, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.

In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

Archimedean solid

Archimedean solid

Archimedean solid

Archimedean solid

Archimedean solid

Archimedean solid

polyhedron which has regular polygons as faces and is vertex-transitive

In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges, and 6 vertices. Its vertex figure is a crossed quadrilateral. Its Coxeter–Dynkin diagram is (although this is a double covering of the tetrahemihexahedron).

self-intersecting uniform polyhedron

polyhedron with 32 faces

polyhedron with 92 faces

thumb|3D model of a dodecadodecahedron In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36. It is the rectification of the great dodecahedron (and that of its dual, the small stellated dodecahedron). It was discovered independently by , and .

polyhedron with 24 faces

polyhedron with 18 faces

polyhedron with 104 faces

polyhedron with 62 faces

polyhedron with 18 faces

polyhedron with 44 faces

polyhedron with 84 faces

nonconvex uniform polyhedron

thumb|3D model of a cubohemioctahedron In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15. It has 10 faces (6 squares and 4 regular hexagons), 24 edges and 12 vertices. Its vertex figure is a crossed quadrilateral.

polyhedron with 26 faces

polyhedron with 84 faces

nonconvex uniform polyhedron

polyhedron with 42 faces

polyhedron with 22 faces

polyhedron with 124 faces

polyhedron with 62 faces

polyhedron with 44 faces

polyhedron with 112 faces

polyhedron with 92 faces

polyhedron with 24 faces

polyhedron with 18 faces

polyhedron with 32 faces

polyhedron with 104 faces

polyhedron with 26 faces

thumb|3D model of a rhombidodecadodecahedron In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces (30 squares, 12 pentagons and 12 pentagrams), 120 edges and 60 vertices. It is given a Schläfli symbol t0,2, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

polyhedron with 112 faces

polyhedron with 44 faces

thumb|3D model of an icosidodecadodecahedron In geometry, the icosidodecadodecahedron (or icosified dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U44. It has 44 faces (12 pentagons, 12 pentagrams and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is a crossed quadrilateral.

polyhedron with 44 faces

polyhedron with 20 faces

polyhedron with 32 faces

polyhedron with 92 faces

polyhedron with 24 faces

polyhedron with 44 faces

polyhedron with 204 faces

polyhedron with 52 faces

polyhedron with 42 faces

polyhedron with 22 faces

thumb|3D model of a rhombicosahedron In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. It has 50 faces (30 squares and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is an antiparallelogram.

polyhedron with 32 faces

polyhedron with 26 faces

uniform polyhedron with dihedral symmetry