Out of Ze Blue #2

In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. It can be found in the application of geodesic dome structures such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It is an example of an Archimedean solid, as well as a Goldberg polyhedron.

The truncated icosahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. It has the same symmetry as the regular icosahedron, the icosahedral symmetry, and it also has the property of vertex-transitivity. The polygonal faces that meet for every vertex are one pentagon and two hexagons, and the vertex figure of a truncated icosahedron is 5 * 6^2. The truncated icosahedron's dual is pentakis dodecahedron, a Catalan solid, shares the same symmetry as the truncated icosahedron.

In this Archimedean Solid, if the edges are curved and it resembles a spherical shape, it will result in the creation of an everyday object in most households.

Another type of this everyday object can be a chamfered dodecahedron.

A chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed as a chamfer (edge-truncation) of a regular dodecahedron. The pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron.

It is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron. It can more accurately be called an order-5 truncated rhombic triacontahedron because only the order-5 vertices are truncated.

Both the truncated icosahedron and the chamfered dodecahedron possess either 120-160 cells but in these everyday objects they are enlarged to form 12 pentagons and 20 hexagons, both regular, to make the distinct appearance.

Nets of solids below.

The object is found mostly in households of sports enthusiasts or households having children.

ID everyday object.