Distances Between H and neighboring C
H and C
distances are (closest to farthest): Blue 1.0A, Green 1.33A, White 1.629A, Red 1.634A, Brown 1.89A
complete list can found here, first column is the number of the carbon atom (starting from 0 for the first carbon in the xyz file), second column is the distance computed.
H2 and H and C
the single atom,

the H2 atoms,

** Correction: distances re-computed according to the moving carbon reveal the following:
for H#1 distances are (C#7) 1.06A, (C#20) 1.81A, (C#3) 1.94A
for H#2 distances are (C#20) 1.78A, (C#34) 1.79A, (C#56) 1.81A
for H#3 distances are (C#7) 1.76A, (C#21) 1.76A, (C#35) 1.82A
We have symetery!
Clearly one sees that for the H2 distances are the same for the closest neighbors (with very slight deviations that could be miscalculations), also, the distance for the first C-H is the same whether it is a just an H or H2+H.
calculation list
H2 and C
atom H1

atom H2

distances calculated are (blue closest nearest neighbor (n.n.)) ~1.45A
(green 2nd n.n.) ~1.57A +/- 0.01A
(white 3rd n.n.) ~1.94A +/- 0.01A
center of the H2 bond

distances calculated are (blue closest nearest neighbor (n.n.)) ~1.47A
(green 2nd n.n.) ~2.30A +/- 0.01A
complete list here, relevant xyz-file here.