For the silicon atom at fractional (0,0,0), find every atom in its shortest-distance nonzero coordination shell. Give the coordination number, shell distance, each neighbor as basis-row plus integer-cell translation, and all distinct neighbor-center-neighbor angles. What coordination polyhedron does this geometry form?

Use the supplied periodic conventional cubic cell, not an isolated XYZ cluster. Cartesian XYZ coordinates are in angstrom; 1 nm=10 angstrom. XYZ atom rows start at one after the two header lines. Fractional positions below are exact; each listed basis atom has occupancy 1. Cell vectors are (a,0,0),(0,a,0),(0,0,a); all angles90 degrees. Crystal images are r_j+a*(n_x,n_y,n_z) for integer n. No relaxation, defects, thermal motion or finite crystallite envelope is supplied.
silicon S0006: a=5.43070 angstrom. Row / element / fractional x,y,z:
1 Si 0 0 0
2 Si 0 1/2 1/2
3 Si 1/4 1/4 1/4
4 Si 1/4 3/4 3/4
5 Si 1/2 0 1/2
6 Si 1/2 1/2 0
7 Si 3/4 1/4 3/4
8 Si 3/4 3/4 1/4

Search n_x,n_y,n_z in {-1,0,1}; this range suffices for the requested nearest shell. Exclude only the central atom at its own location. Group distances within 0.00001 angstrom; report distances in nm to four decimals and angles in degrees to two decimals. Do not count only atoms displayed inside the single stored cell.

Attachment S0006:
8
Coordinates in angstrom; atoms numbered from 1.
Si 0.00000000 0.00000000 0.00000000
Si 0.00000000 2.71535000 2.71535000
Si 1.35767500 1.35767500 1.35767500
Si 1.35767500 4.07302500 4.07302500
Si 2.71535000 0.00000000 2.71535000
Si 2.71535000 2.71535000 0.00000000
Si 4.07302500 1.35767500 4.07302500
Si 4.07302500 4.07302500 1.35767500