In this article the operation of a composite Yb:YAG/YAG asymmetric hexagonal thin disk laser is optimized. This structure consists an Yb:YAG thin sheet as laser material and a diffusion bonded undoped material on top of thin sheet. Three diodes are placed outside the asymmetric hexagonal shape disk, and the emitting light is coupled via three lens ducts through its three edges and propagates through the disk along the zigzag path and repeatedly passes the gain medium, thus pump uniformity and absorption efficiency are improved. A Monte Carlo ray tracing code and Finite Element Analysis is utilized for calculation of absorbed pump density and volume temperature distribution and also thermal and mechanical stresses, respectively. Finally the output power is calculated. The triplet designing parameters, namely absorbed power efficiency, absorption uniformity and temperature distribution are optimized. Results show this edge-facet pumped geometry is a high efficient configuration for thin gain lasers.