  We show that new silicon crystalline phases, observed in the experiment with
the laser-induced microexplosions inside silicon crystals (Rapp et al. // Nat.
Commun. 6, 7555 (2015)), are all superstructures of a disordered high-symmetry
phase with $Ia\bar{3}d$ cubic space group, as well as known for many years
phases $bc8$ (Si-III) and $r8$ (Si-XII). The physics of this phenomenon is
rather nontrivial: The $bc8$-like superstructures appear as regularly ordered
patterns of switchable atomic strings, preserving everywhere the energetically
favorable tetrahedral coordination of silicon atoms. The variety of
superstructures arises because each string can be switched between two states
independently of the others. An infinite family of different phases can be
obtained this way and a number of them are considered here in detail. In
addition to the known $bc8$, $bt8$, and $r8$ crystals, 128 tetrahedral
structures with 16 (6 phases), 24 (22 phases), and 32 (100 phases) atoms per
primitive cell are generated and studied, most of them are new ones. For the
coarse-grain description of the structures with two possible states of
switchable strings, the black/white (switched/nonswitched) Shubnikov symmetry
groups has been used. An ab initio relaxation of the atomic positions and
lattice parameters shows that all the considered phases are metastable and have
higher density and energy relative to the $bc8$ phase at the ambient pressure.
A possible scenario for appearance of those phases from the high-temperature
amorphous phase is discussed.
