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An entry in Fortnightly Topic Challenge #48: Unusual tag mix

I was trying to study some geometry, but I just can't seem to wrap my head around all this mathematical mumbo jumbo. Can you help me out?

  1. Many an object of this type are familiar to geometers! (8)
  2. A famous mathematician returned to sign with hat (6)
  3. Legs itch, tea spilled (7)
  4. A ring is nearly invalid inside a bum (7)
  5. A parallelogram partially gets started backtracking on a weekday (6)
  6. Concise line made more concise line on regular polygon (7)

The above postulates are supposed to help me solve the below equation, which I think my professor called the Vigenere Theorem or something... I don't quite remember because it was early and I was very sleepy.

  • Y vxseztmxzfcgu lu c nxbppn seu nlutxre qjfwtz emvn kwjrbmvx
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Partial answer: all but two clues solved

The cryptic clue answers are:

TRIANGLE? (This looks like a cryptic definition, but "familiar" or "family" don't seem to have any special meaning in geometry.)
EUCLID (reversal of CUE, plus LID)
CATHETI (anagram of "itch tea", definition "legs")
ANNULUS (NUL(-l) inside ANUS)
GNOMON (start of "Gets"; reversal of ON; MONday)
??? (Answer likely hexagon / octagon / nonagon / decagon / megagon - the last seems plausible given that "line" could be GAG (as in a joke). If "Concise line made more concise" could give ME, that would complete the wordplay.)

I've tried

decrypting the given string with all the answers concatenated. This didn't seem to give anything useful. I've also tried decrypting with the guesses I have so far, and then breaking the remaining Vigenere cipher with usual cryptographic techniques. This also didn't work, so either that's not correct either, or both TRIANGLE and MEGAGON are wrong.

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    $\begingroup$ I normally wouldn't post a partial answer like this, but the puzzle's been sitting out for a day and there haven't been any answers, even though it's relatively small. If anyone else finishes this off, feel free to take my explanations for the clues I've solved, and post your own answer. $\endgroup$
    – Deusovi ♦
    Jan 29, 2021 at 19:59
  • $\begingroup$ I had rot13("dhnagvgl" nf n qbhoyr qrsvavgvba) for #1, but the subject-verb agreement didn't quite match up $\endgroup$
    – samm82
    Jan 29, 2021 at 20:01
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    $\begingroup$ On the last clue, what is your interpretation of the word "regular"? It seems superfluous unless used for wordplay or used to clue an identifiably regular polygon like a square. $\endgroup$
    – hexomino
    Jan 29, 2021 at 20:08
  • $\begingroup$ The two possible 7-letter regular polygons I found were rot13(eubzohf naq qvnzbaq), but I couldn't get wordplay to work for them, and even classifying them as regular is a stretch $\endgroup$
    – samm82
    Jan 29, 2021 at 20:11

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