  We present a photometric and spectroscopic study of a reddened type Ic
supernova (SN) 2005at. We report our results based on the available data of SN
2005at, including late-time observations from the Spitzer Space Telescope and
the Hubble Space Telescope. In particular, late-time mid-infrared observations
are something rare for type Ib/c SNe. In our study we find SN 2005at to be very
similar photometrically and spectroscopically to another nearby type Ic SN
2007gr, underlining the prototypical nature of this well-followed type Ic
event. The spectroscopy of both events shows similar narrow spectral line
features. The radio observations of SN 2005at are consistent with fast
evolution and low luminosity at radio wavelengths. The late-time Spitzer data
suggest the presence of an unresolved light echo from interstellar dust and
dust formation in the ejecta, both of which are unique observations for a type
Ic SN. The late-time Hubble observations reveal a faint point source coincident
with SN 2005at, which is very likely either a declining light echo of the SN or
a compact cluster. For completeness we study ground-based pre-explosion
archival images of the explosion site of SN 2005at, however this only yielded
very shallow upper limits for the SN progenitor star. We derive a host galaxy
extinction of $A_{V} \approx 1.9$ mag for SN 2005at, which is relatively high
for a SN in a normal spiral galaxy not viewed edge-on.
