El rombicuboctaedre està format per 18 quadrats i 8 triangles equilàters.

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

Volume: 2*(6+5*sqrt(2))/3

Per un rombicuboctaedre d'aresta unitat tenim:

  • Rcircumscrita = \(\frac{\sqrt{5+2\sqrt{2}}}{2}\)
  • Rtangent arestes = \(\frac{\sqrt{2\left(2+\sqrt{2}\right)}}{2}\)
  • Volum = \(\frac{2\left(6+5\sqrt{2}\right)}{3}\)

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