Quasiregular polyhedra

A cuboctahedron, rectified cube, or rectified octahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e., an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron.

Catalan polyhedron

thumb|3D model of an icosidodecahedron

Catalan polyhedron

semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex

a tiling of the plane by regular hexagons and equilateral triangles, with each edge separating both types of shape

tiling of the plane with 60° rhombi

semiregular tiling of the hyperbolic plane