LED Circuit 24 LED's

[prevan850]

I am making a circuit my constraints are space and shape of my circuit. I am basically making a ring (or a circle) of LED's, kind of like a flash light. My plan is to make an outer ring witch will be my positive lead in and that will run through 2 LED's in series. Then my inner ring will be my negative and lead back to my power source. I will have an array of 12 "2 LED" series in parallel. (i hope that makes sense). Anyway my question is what size resistor will i need. i believe i have done the math right.

What my circuit looks like (something like this but i will have 12 series and 24 LED's
------ LED---LED------ neg
pos ------- R ------ LED---LED------ neg
------ LED---LED------ neg


MATH

Power suuply = 12v
LED V = 3.2v
LED current = 20mA

R = (12-(3.2*2))/((0.020*2)*12)
R = 11.25 ohms

Wattage of resistor
w = (12-(3.2*2))*((0.020*2)*12)
w = 2.592 watts

so i would need a 2.59 watt resistor with 11.25 ohms of resistance

is this true?