L'octaedre truncat s'obté tallan els 6 vèrtexs d'un octaedre regular i està format per 6 quadrats i 8 octàgons regulars.
Coordenades dels vèrtexs
Per un octaedre truncat d'aresta unitat, les coordenades dels seus vèrtexs són:
- \(V_1=\left(a,0,b\right)\)
- \(V_2=\left(a,0,-b\right)\)
- \(V_3=\left(-a,0,b\right)\)
- \(V_4=\left(-a,0,-b\right)\)
- \(V_5=\left(b,a,0\right)\)
- \(V_6=\left(b,-a,0\right)\)
- \(V_7=\left(-b,a,0\right)\)
- \(V_8=\left(-b,-a,0\right)\)
- \(V_9=\left(0,b,a\right)\)
- \(V_{10}=\left(0,b,-a\right)\)
- \(V_{11}=\left(0,-b,a\right)\)
- \(V_{12}=\left(0,-b,-a\right)\)
- \(V_{13}=\left(0,a,b\right)\)
- \(V_{14}=\left(0,a,-b\right)\)
- \(V_{15}=\left(0,-a,b\right)\)
- \(V_{16}=\left(0,-a,-b\right)\)
- \(V_{17}=\left(b,0,a\right)\)
- \(V_{18}=\left(b,0,-a\right)\)
- \(V_{19}=\left(-b,0,a\right)\)
- \(V_{20}=\left(-b,0,-a\right)\)
- \(V_{21}=\left(a,b,0\right)\)
- \(V_{22}=\left(a,-b,0\right)\)
- \(V_{23}=\left(-a,b,0\right)\)
- \(V_{24}=\left(-a,-b,0\right)\)
on:
- \(a=\frac{\sqrt{2}}{2}\)
- \(b=\sqrt{2}\)
