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.

A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding spherical polyhedron. The most familiar spherical polyhedron is the soccer ball, thought of as a spherical truncated icosahedron.

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. 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).

A truncated icosahedron is constructed by cutting off the vertices of an icosahedron in a way, so that every edge has the same length. This solid is famous as soccer ball shape and from the Bucky Ball (Buckminsterfullerene, C 60 molecule). Its dual body is the pentakis dodecahedron. Enter one value and choose the number of decimal places.

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 creates 12 new pentagon faces, and leaves the original 20 triangle faces as regular hexagons.

The truncated icosahedron (common soccer ball or C 60) contains a rectangle with edges in the ratio 3φ:1. The icosidodecahedron has a radius:edge of φ:1. Credit: page 341 in Designa. The Icosahedron is made of equilateral triangles arranged into five-sided pentagonal shapes called icosahedral caps.

Imagine that I have a truncated icosahedron consisting of 60 identical vertices, each of degree deg(v) = 3 d e g (v) = 3, and fixed edge length L L. I'd like to assign some constant curvature or bending angle θ θ to each edge s.t. I can deform the truncated icosahedron into …

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.

Oct 5, 2019 · – the truncated icosahedron can be obtained by cutting off the 12 vertices with the formation of facets in the form of regular pentagons. The number of vertices of the new polyhedron is increased 5 times (12×5=60), 20 triangular faces become regular hexagons (all faces become 20+12=32), and the number of ribs increases to 30+12×5=90;

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. It is the Goldberg polyhedron GV(1,1), containing pentagonal and hexagonal faces.