Geometric Relations
The truncated icosahedron easily verifies the Euler characteristic:
- 32 + 60 − 90 = 2.
With unit edges, the surface area is (rounded) 21 for the pentagons and 52 for the hexagons, together 73 (see areas of regular polygons).
Read more about this topic: Truncated Icosahedron
Famous quotes containing the words geometric and/or relations:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“As death, when we come to consider it closely, is the true goal of our existence, I have formed during the last few years such close relations with this best and truest friend of mankind, that his image is not only no longer terrifying to me, but is indeed very soothing and consoling! And I thank my God for graciously granting me the opportunity ... of learning that death is the key which unlocks the door to our true happiness.”
—Wolfgang Amadeus Mozart (1756–1791)