Truncated Icosahedron - Dimensions

Dimensions

If the edge length of a truncated icosahedron is a, the radius of a circumscribed sphere (one that touches the truncated icosahedron at all vertices) is:

where φ is the golden ratio.

This result is easy to get by using one of the three orthogonal golden rectangles drawn into the original icosahedron (before cut off) as the starting point for our considerations. The angle between the segments joining the center and the vertices connected by shared edge (calculated on the basis of this construction) is approx. 23.281446°.

Read more about this topic:  Truncated Icosahedron

Famous quotes containing the word dimensions:

    It seems to me that we do not know nearly enough about ourselves; that we do not often enough wonder if our lives, or some events and times in our lives, may not be analogues or metaphors or echoes of evolvements and happenings going on in other people?—or animals?—even forests or oceans or rocks?—in this world of ours or, even, in worlds or dimensions elsewhere.
    Doris Lessing (b. 1919)

    Why is it that many contemporary male thinkers, especially men of color, repudiate the imperialist legacy of Columbus but affirm dimensions of that legacy by their refusal to repudiate patriarchy?
    bell hooks (b. c. 1955)

    Words are finite organs of the infinite mind. They cannot cover the dimensions of what is in truth. They break, chop, and impoverish it.
    Ralph Waldo Emerson (1803–1882)