Poliedres arquimedians

Característiques bàsiques

• Cares = 26
• Arestes = 48
• Vèrtexs = 24

Coordenades dels vèrtexs

Per un rombicuboctaedre d'aresta unitat, les coordenades dels seus vèrtexs són:

• \(V_1=\left(a,a,b\right)\)
• \(V_2=\left(a,a,-b\right)\)
• \(V_3=\left(a,-a,b\right)\)
• \(V_4=\left(a,-a,-b\right)\)
• \(V_5=\left(-a,a,b\right)\)
• \(V_6=\left(-a,a,-b\right)\)
• \(V_7=\left(-a,-a,b\right)\)
• \(V_8=\left(-a,-a,-b\right)\)
• \(V_9=\left(b,a,a\right)\)
• \(V_{10}=\left(b,a,-a\right)\)
• \(V_{11}=\left(b,-a,a\right)\)
• \(V_{12}=\left(b,-a,-a\right)\)
• \(V_{13}=\left(-b,a,a\right)\)
• \(V_{14}=\left(-b,a,-a\right)\)
• \(V_{15}=\left(-b,-a,a\right)\)
• \(V_{16}=\left(-b,-a,-a\right)\)
• \(V_{17}=\left(a,b,a\right)\)
• \(V_{18}=\left(a,b,-a\right)\)
• \(V_{19}=\left(a,-b,a\right)\)
• \(V_{20}=\left(a,-b,-a\right)\)
• \(V_{21}=\left(-a,b,a\right)\)
• \(V_{22}=\left(-a,b,-a\right)\)
• \(V_{23}=\left(-a,-b,a\right)\)
• \(V_{24}=\left(-a,-b,-a\right)\)

on:

• \(a=\frac{1}{2}\)
• \(b=\frac{1+\sqrt{2}}{2}\)

Característiques avançades

Per un rombicuboctaedre d'aresta unitat tenim:

• R_circumscrita = \(\frac{\sqrt{5+2\sqrt{2}}}{2}\)
• R_{tangent arestes} = \(\frac{\sqrt{2\left(2+\sqrt{2}\right)}}{2}\)
• Volum = \(\frac{2\left(6+5\sqrt{2}\right)}{3}\)