El dodecaedre regular està format per dotze pentàgons regulars. En la figura 3D pots moure'l per observar-lo des de diferents punts de vista.
Coordenades dels vèrtexs
Per un dodecaedre regular d'aresta unitat, les coordenades dels seus vèrtexs són:
- \(V_1=\left(0,a,c\right)\)
- \(V_2=\left(0,a,-c\right)\)
- \(V_3=\left(0,-a,c\right)\)
- \(V_4=\left(0,-a,-c\right)\)
- \(V_5=\left(c,0,a\right)\)
- \(V_6=\left(c,0,-a\right)\)
- \(V_7=\left(-c,0,a\right)\)
- \(V_8=\left(-c,0,-a\right)\)
- \(V_9=\left(a,c,0\right)\)
- \(V_{10}=\left(a,-c,0\right)\)
- \(V_{11}=\left(-a,c,0\right)\)
- \(V_{12}=\left(-a,-c,0\right)\)
- \(V_{13}=\left(b,b,b\right)\)
- \(V_{14}=\left(b,b,-b\right)\)
- \(V_{15}=\left(b,-b,b\right)\)
- \(V_{16}=\left(b,-b,-b\right)\)
- \(V_{17}=\left(-b,b,b\right)\)
- \(V_{18}=\left(-b,b,-b\right)\)
- \(V_{19}=\left(-b,-b,b\right)\)
- \(V_{20}=\left(-b,-b,-b\right)\)
on:
- \(a=\frac{1}{2}\)
- \(b=\frac{1+\sqrt{5}}{4}\)
- \(c=\frac{3+\sqrt{5}}{4}\)