In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. Intuitively, it may be regarded as footballs (or soccer balls) that are typically patterned with white hexagons and black pentagons.

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement . It is also the uniform polyhedron with Maeder index 25 (Maeder 1997), Wenninger index 9 (Wenninger 1989), Coxeter index 27 (Coxeter et al. 1954), and Har'El index 30 (Har'El 1993). It has Schläfli symbol t and Wythoff symbol .

What is a truncated icosahedron? Why called a soccer ball? Download a shape net of a truncated icosahedron for DIY assembly. Mathematical properties of a truncated icosahedron. How many faces? Make order a set to DIY.

Truncated icosahedron Convex regular icosahedron. A truncated icosahedron is an Archimedean solid. A regular icosahedron is made of 20 faces. When a regular icosahedron is truncated, this means that each "corner" (or vertex) is replaced by a …

Properties of the truncated icosahedron: Number of faces, edges and dihedral angle measure. The truncated icosahedron is created by truncating (cutting off) the tips of the icosahedron one third of the way into each edge. 32 total faces: 12 regular pentagons and 20 regular hexagons. 60 vertices: 2 hexagons and 1 pentagon. 90 edges. Dihedral angles:

The truncated icosahedron is an Archimedean solid. It comprises 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. This polyhedron can be constructed from an icosahedron with the 12 vertices truncated (cut off) such that one third of each edge is cut off at each of both ends.

This process shortens the side lengths of the edges in the original icosahedron by the same amount. Notice that it also doubles the number of edges -- changing the green triangular faces of the icosahedron (left) into green hexagonal faces in the truncated icosahedron (right).

The truncated icosahedron, or ti, is one of the 13 Archimedean solids. It consists of 12 pentagons and 20 hexagons. Each vertex joins one pentagon and two hexagons. As the name suggests, it can be obtained by the truncation of the icosahedron. It can also be thought of as the shape of a soccer ball, but not all soccer balls look like this.

truncated icosahedron (60 + 32 = 90 + 2 ). (b) The sum of the angles at the vertices of the polygons that meet at any vertex of the polyhedron is necessarily less than 360o, else it would just flatten out. The shortfall, i.e., the difference between 360o and the sum as mentioned above, is termed the angular defect of the said vertex.

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons. It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.