No all time zones are used in the Antarctic. As you get closer to the South Pole, the time zones converge and become meaningless. For practical purposes time zones are usually based on territorial claims; however, many stations use the time of the country they are owned by or the time zone of their supply base
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Your question did not ask how many time zones were "used". It explicitly asked if 24 time zones "intersected" in Antarctica. While 24 time zones are not used in Antarctica, they do technically intersect at the pole. Therefore, the original poster was correct in answering your original question. Your little map above shows time zones actually used in Antarctica. Again, that's not what so specifically asked which the point you made in post #140 ("You did not answer the question as asked").
"Technically, Antarctica, and the North Pole, fall under all time zones currently followed by the rest of the world. This is because the longitude lines that are used to define time zones all meet at the two poles."
http://www.timeanddate.com/time/time-zone-antarctica.html
"At the South Pole base, you can literally walk ... going through every single time zone..." - interview with Tamsin Gray, British Antarctic Survey meteorologist at the Rothera base in Antarctica (see video at 1:15 mark)
http://www.bbc.com/news/world-12841278
"Theoretically Antarctica would be located in all time zones."
https://en.wikipedia.org/wiki/Time_in_Antarctica