edit: This answer adds one more piece to the puzzle, at least for data.

For navigation, I believe GPS covers the poles.

For data, there is at least Iridium (see answers to What (actually) makes Iridium “the world's only truly global mobile satellite communications company”? but there may be government satellites for government sponsored bases as well, but I'm not sure.

And after reading @Tristan's comment below Has there been any satellites that used an 'upside-down' Molniya orbit? I realized that the GEO band is way below the horizon for the poles.

So I'd like to know what satellites are used by bases on Antarctica for scientific data up/down link, internet for science and personal use, and for watching TV, especially those near or at the South Pole?

For example, I found this image of a GEO satellite receiving dish in this Reddit, taken "outside Anchorage" and so only at about 61 degrees North latitude (cropped, click for full size) This kind of antenna (often) uses an offset parabola, so the incident angle is somewhat higher that you might guess by looking at it. The majority of antarctica is beyond 60 degrees South though. Note that those elevation angles are maximum values for a GEO position equal to your longitude. As one gets closer to the poles, the window to useful GEO positions closes quite rapidly.

Table and diagram from NOAA:

latitude  max elevation (Ellipsoidal model of Earth, degrees)
   60           22.0
   65           16.7
   70           11.5
   75            6.4
   80            1.4

Satellite dish near Anchorage cropped GEO Look angles

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    $\begingroup$ Start with usap.gov/technology/contentHandler.cfm?id=1982. There is a list of satellites and times they are available. -MBM $\endgroup$ – MBM Feb 13 '18 at 20:29
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    $\begingroup$ GPS does cover the South Pole, see. But for best satellite geometry, there should be one vertically above the pole, but there are no GPS satellites on a polar orbit. The precision of the position is somewhat reduced. $\endgroup$ – Uwe Feb 13 '18 at 20:34
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    $\begingroup$ en.wikipedia.org/wiki/Telecommunications_in_Antarctica $\endgroup$ – jwdonahue Feb 13 '18 at 21:58
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    $\begingroup$ Can someone elaborate why a question about access to commercial satellites for personal and entertainment use, at the south pole where the GEO constellation is invisible, is off-topic here? Much of the entire space industry was funded by people watching TV. We have dozens of questions about communications satellites in GEO orbits. Now I'm asking about geographic location on the Earth where that orbit is inaccessible, and alternative orbits need to be used. Are questions about the commercial and civilian uses of space going to be off-topic from now on? $\endgroup$ – uhoh Feb 14 '18 at 0:36
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    $\begingroup$ uhoh, satellites are used for operational and scientific data first, but the bandwidth is available for personal use after that. So, skype is possible, but I do not know about other phone connections. McMurdo does have phones, and TV. I think ATS-3 finally died, but it could support a phone call. -MBM $\endgroup$ – MBM Feb 14 '18 at 0:54

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