The packet radio satellites offer a different challenge and the antennas used here include - quad helix, eggbeater, lindenblad and in the case of some ‘gateway’ stations - fully steerable beams (yagis and/or helicals).
The first three antenna type can be ‘homebrewed’ for amateur radio service with basic hand tools and provide good omnidirectional performance on LEO satellites.
Construction details of suitable antenna systems are beyond the scope of this site and may be found in Oscar News, The Amsat Journal, The Satellite Experimenters Handbook and the ARRL Handbook.