Find the number of triangle in this figure?

Naming the edges of the figure:

We manually count the triangles as

(GLK, DLJ, DJM, HMN, QRE, IRA, IPA, FPO)

(BDO,CDQ, DLM, PRA, KFI, NEI, HJI, GJI,DKI, DNI)

(DIE, DFI, DOA, DQA, GHI) 

(DCA, DBA) (DEF) (ABC)

 8 + 10 + 5 + 2 + 1 + 1 = 27