The answer is:
Consider the riddle as a person. So, it stated head, face, back, thighs, feet and the rest which means:
Head = Title
Face = first Two Lines
Back = next Two Lines
Thighs = next Two Lines
Feet = next Two Lines
Rest = rest of the Lines
There are patterns like pentagonal, squares, lazy caterer, fibonacci, look and say in the riddle. The words jantar and mantar (or yantra and mantra) means calculation instrument
Never try to ignore, b'lieve in the pentagonal head of mine.
It gives you my first three, out of nine.
First we need to take the pentagonal numbers out of the title, which is the head of the riddle. So, we take the letters 1, 5 and 12. We get: s, r, i
As a rightful person, look and say to my face.
Three of these and thrice more, completes your half a race.
Then, we use the look-and-say sequence on the face of the riddle, which is composed of the first two lines. We get: n, i, v
Rammle is what you've found. Now get the squares off my back.
Earn three more and you have left nine more to crack.
Now, we take the squares off your back, which is the next two lines: a, s, a
We have the first part, yay!
An ultimate, lazy and outspoken Mr.Caterer, who lives on my thighs.
Force him to give you the next three, if he denies.
We first use the lazy caterer's sequence on the thighs: so we take the letters 1, 2, 4 from the line Rammle is what you've found..., so we obtain the letters r, a, m
Jantar Mantar all above, while the headless famous lives on my feet,
Then the headless famous refers to the Fibonacci sequence, without the first term (headless). So, we get the letters 1, 2 and 3 which gives us a, n, u.
Three again and seek three from the first of the rest and you shall tribute me and cherish this amazing feat!
Finally, we seek three from the first of the rest, that's to say we just need to take the first three letters of the last sentence (Jantar Mantar all above...), which gives us j, a, n
And we get it all together to have the final answer! Complex but cool riddle!