Punch a small hole at either end of all the straws to allow for the fasteners to be connected easily.
Create six pentagons by connecting the ends of five of the shortest straws together, and fasten using a brad fastener at the center of the pentagon. This will look like a star, with the fastener in the middle and five straws radiating outward to form the pentagon figure. Make six of these and set aside.
Make fifteen hexagons by connecting the ends of the longest straws together, and fasten using a brad fastener at the center of the hexagon. These will also look like a star, with the fastener in the middle and six straws radiating outward to form the hexagon figure. Make fifteen of these and set aside.
Connect five hexagons to each side of one pentagon using one medium sized straw to join the sides together. Use brad fasteners for this.
Connect the other five remaining pentagons using medium length straws to the outside edges of your now partial dome.
Connect the remaining ten hexagons to the outside of this structure using the medium length straws.