Question

O icosoedro é um poliedro convexo de 20 faces triangulares.Quantas são os vertices e as arestas?

Answer 1

$\mathrm{F=20\ (triangulares)}\\\\ \textrm{Pela rela\c{c}\~ao das arestas, teremos que:}\\\\ \mathrm{A=\dfrac{n_1.f_1}{2}=\dfrac{3.20}{2}=\dfrac{60}{2}=30\ arestas}\\\\ \textrm{Pela rela\c{c}\~ao de Euler, teremos que:}\\\\ \mathrm{V+F=A+2\ \to\ V+20=30+2}\\ \mathrm{V=32-20\ \to\ V=12\ v\'ertices}\\\\ \boxed{\mathbf{A=30\ \ \|\ \ V=12\ \ \|\ \ F=20}}$