Find the Number of Triangles

[OmCheeto]

Wondering if this is how Garret Lissi got his start.

{edit}
I finally counted 160....

 

[bob012345]

My artwork isn’t as pretty but here it is anyway. Each size triangle is represented only once. There are four shapes out of 22 that are left-right symmetric wrt to the whole figure are multiplied by 4 and the rest by 8.

 

[OmCheeto]

My artwork isn’t as pretty but here it is anyway. Each size triangle is represented only once. There are four shapes out of 22 that are left-right symmetric wrt to the whole figure are multiplied by 4 and the rest by 8.
...

At least you didn't screw up. I've just noticed multiple errors in my image. Glad I said it would take me a week to count all these stinkin' triangles!

 

[FactChecker]

One take-away from this is how rapidly a simple problem can become unmanageable. Combinatorial problems grow exponentially and the slightest modification can make the calculations very difficult. By "unmanageable", I mean it might take a supercomputer decades to solve.