Current model networks for amorphous Ge contain five-membered rings and pentagonal dodecahedra to explain why in the radial distribution function the third peak of the diamond structure is missing. By presenting an algorithm based on a decoration of the three-dimensional Penrose quasilattice, we prove that this local pentagonal symmetry can be extended globally to an icosahedral quasicrystalline tetracoordinated network. Its structural elements and topological properties coincide with previous hand-built models of random networks. Thus it is suitable for simulating bulk properties of amorphous semiconductors.