I must issue a word of caution dear traveler. As your journey nears its end, you have one final obstacle to overcome. Ahead lies the gate of the guardians. As you might suspect, the gate is protected by two guardians. One always lies and one always tells the truth. In order to ensure your safe passage across the threshold of the gate, you must determine their password.
Each guardian only knows the other's half of the password along with how to determine their own. They will supply this information to you upon request.
However, there is one very important rule: you may only speak to one of the guardians. Choose wisely dear traveler, for this decision, could very well be your last.
As you approach the gate you notice an inscription:
This gate is equidistant from the farthest edges of the world.
Note: Please follow the rules and only read the section for one of the guardians. While there's no shame in looking at both, the puzzle is more fun to solve by the rules. If you do look, let us know when you chose to do so in your answer, you won't be disqualified.
Left Guardian
You approach the guardian on the left:
Ahhh, wise choice dear traveler.
I always tell the truth.
Nineteen, five, twenty. Start in the middle of a icosikaihexagon; two, seven, seven.
Right Guardian
You approach the guardian on the right:
Ahhh, wise choice dear traveler.
I always tell the truth.
Six, fifteen, six. Navigate between the edges of two dodecagons; six, seven, eight.
After approaching the guardian of your choosing and hearing what they have to say, both guardians sternly demand; what's the password?!
Note: Your answer must include which guard you spoke with, and your determination on whether or not they were the liar, along with what the password is, in order to get the checkmark.